Skinwalkers are humanoids that have been touched by the taint of a lycanthrope somewhere in their heritage, and in some cases this grants some really fun abilities. There is a "generic" skinwalker race and themed versions, just like there are for Aasimar and Tieflings, so this will be a relatively long article!
Ability Scores: The standard ability score modifiers for Skinwalkers are +2 Wisdom and -2 Intelligence, with a floating +2 to any physical ability score that is assigned every time they take on their "bestial form". This makes Inquisitor, Druid, and pretty much any martial class a good choice for them.
Type: Skinwalkers are humanoids with the skinwalker and shapechanger subtypes, and while there are a few spells that affect shapechangers only, for the most part you can treat them like any core race.
Size: Skinwalkers are the same size as humans.
Speed: Skinwalkers move at the same speed as humans.
Animal-minded: +2 to Handle Animal and on wild empathy checks isn't that exciting, unless you happen to be a Druid.
Change shape: Skinwalkers have the ability to take on a bestial form which grants them a floating bonus to any one physical ability score (Str, Dex, or Con) and also gives them a bestial feature, chosen from a list. For the basic skinwalker, this list includes a pair of claw attacks dealing 1d4 base damage each, darkvision 60 ft, or a +1 racial bonus to natural armor. They unfortunately also take a -4 to Charisma checks and Charisma-based skill checks while in this form, however, which means you're not going to be Diplomancing any encounters in your bestial form. I would also caution you that, the way it's written, a GM could say that you're taking an actual penalty to Charisma, not just checks, and so then you can essentially never change into your bestial shape as a Sorcerer or Oracle. Overall, though, a floating ability score bonus that you assign each time you shapechange is pretty excellent.
Spell-Like Ability: Basic skinwalkers can cast speak with animals once per day, which is pretty "meh" in my mind.
Low-light Vision: Low-light vision is nice, but not nearly as good as darkvision.
Skinwalkers get several heritage options that are in general a bit stronger than the base skinwalker options, but they obviously go with a specific animal theme.
Bloodmarked (Werebat-kin): These batty skinwalkers make for great arcane spellcasters, Rogues and Ninjas thanks to their constant bonus to Int and sometimes-bonus to Dex. They also get a much more useful spell-like ability than the base skinwalker, obscuring mist 1/day.
Coldborn (Werebear-kin): Skinwalkers prone to hibernation are excellent Barbarians and Monks, since they have a constant Constitution bonus and a bestial Wisdom bonus. They can also gain a climb speed or a bite attack, which can come in handy. The spell-like ability, calm animals 1/day, may come in useful early in the game but will quickly become useless at higher levels.
Ragebred (Wereboar-kin): These guys are absolutely born to be Barbarians, with a bestial bonus to Constitution that stacks with rage, the ability to increase their speed during bestial shape, a gore attack or two hoof attacks, and 6 new Barbarian rage powers available!
Scaleheart (Werecrocodile-kin): Croc-walkers have a bonus to Intelligence inherently, and they gain a Strength bonus during bestial shape, so in my mind their best class option is a Strength-based magus. The spell-like ability is scare 1/day, which is just okay really. They are unique in gaining the ferocity special ability as one bestial shape option, and that's REALLY great for a melee fighter.
Nightskulk (Wererat-kin): Wererat-kin were obviously built around becoming Rogues, with an inherent Int bonus and a bestial Dex bonus, along with 4 new racial Rogue talents available. They can also make for very decent ranged Alchemists. The spell-like ability is even worse than the standard skinwalker option (though you do get more uses per day, whoopie!)... you can cast speak with animals 3/day, but only to talk to rodents.
Seascarred (Wereshark-kin): These guys have bonuses to Wis normally and Con when in bestial form, which stacks nicely with Barbarian rage. For some strange reason, the powers-that-be decided that a racial option with a penalty to Int would make good Magi, so they have a bunch of Magus arcana available that will never get used. They can gain a bite or a swim speed, as well as the ability to breathe underwater, so that could come in handy in a pirate-themed game, that's for sure!
Fanglord (Weretiger-kin): As the only skinwalkers with any sort of Charisma bonus, this will be your option for a skinwalker Sorcerer, Oracle, or Summoner, but remember that you don't want to change to your bestial shape if you are planning to talk to humanoids, because you're still going to have a net -2 to your Charisma-based skill checks in bestial form, even with the bonus +2 you gain by changing (which sucks!) Fanglords uniquely get the see in darkness special ability as an option when in bestial form, which is excellent!
Witchwolf (Werewolf-kin): Werewolves are what most people think of when they think "lycanthrope", thanks to the media's obsession with werewolf-vampire wars or whatever. Werewolf-kin get Strength and Wisdom bonuses, which means you can choose pretty much any martial class, with Inquisitors and Monks gaining the most. You also get a racial bonus to the most important skill in the game, Perception, so that's nice. Finally, magic fang 1/day is super useful if you choose either the bite or claws option when in bestial form, so werewolf-kin is a really good choice overall.
Alchemist: The Bloodmarked, Scaleheart, and Nightskulk heritages all lend themselves positively to alchemy, with Scaleheart being better for melee Dr.Jekyl/Mr.Hyde builds and Nightskulk being better for ranged bomber builds. A Scaleheart alchemist also has access to an exclusive alchemical discovery starting at 6th level, the Psychoactive Bomb. This causes the target penalties to mind-affecting, fear, and several other types of effects, all for the sacrifice of just 1d6 damage. Overall, there are several ways for a skinwalker to make an excellent alchemist. If you are limited to the generic skinwalker, however, you're probably not going to be excellent at alchemy thanks to the -2 to Intelligence.
Barbarian: The Ragebred skinwalker is obviously built specifically to make for brutal barbarians, with a total of 6 new rage powers exclusive to that heritage. They gain a bonus to Constitution that stacks with rage and also increases rage rounds per day, and the Boar's Charge rage power is absolutely sick, giving you unlimited automatic critical hits on successful gore attacks as part of a charge. If you combine this with Greater Beast Totem and haste or a similar ability that grants extra attacks on a full attack, you could get two auto-crit attacks (and apply Critical Feats to each of them) per round. Wow! (If you're stuck with the generic skinwalker, they can still do pretty well, just make sure in either case to pick up Fast Change so that you don't screw up your action economy too badly.)
Bard: The Fanglord skinwalker is the only heritage that gains a boost to Charisma, but don't forget that your Charisma-based skill checks will have a net -2 in bestial form, which includes your Perform checks, which significantly nerfs several bardic performances that rely on Perform checks to set DCs and things like that. You can still do the standard inspire courage and inspire greatness with no penalty, though. Overall, there aren't many ways to make a skinwalker Bard work well, so it's just not the optimal choice.
Cavalier [Samurai]: Skinwalkers make natural Beast Rider cavaliers, and of course it's thematic for a skinwalker cavalier to have a mount related to their heritage. The only heritage that really doesn't work well for cavalier is the Nightskulk because of their Strength penalty. I can especially imagine a Fanglord cavalier riding a tiger mount, using feats like Motivating Display and Violent Diplay to intimidate her foes.
Cleric: Skinwalkers can make fine clerics, though you'll probably want to stay away from the heritages that take a -2 penalty to Wisdom. There's really nothing that makes a skinwalker specifically GOOD at being a cleric, though, so this is just sort of an "if you want to, no problem" type of situation.
Druid: Skinwalkers can make very decent druids for the same reason as clerics, however the bit difference here is that thematically, the shapeshifting fits the druid class much better, and the actual abilities gained from being a skinwalker stack very well with druidic powers. Again, stick with one of the heritages that doesn't give up on Wisdom, and you'll be golden.
Fighter: The bestial features that skinwalkers gain when in bestial form really lend themselves to melee combat, with several options for natural attacks. The Savage Warrior, or the Unarmed Fighter combined with Feral Combat Training are both excellent options to make the most of those bestial features. You can also make an excellent archer build using the Bloodmarked, Nightskulk, or Fanglord heritages.
Gunslinger: A skinwalker can make a very nice gunslinger if Dex is the focus, so you're really looking at vanilla skinwalker, Bloodmarked, Nightskulk, or Fanglord as options here. There aren't any special archetypes or powers here that make them work better than any other Dex-y race, though.
Inquisitor: For the same reasons as the druid, a skinwalker inquisitor can turn out to work extremely well. But like the cleric, there's nothing really specific that makes them better than any other race with a Wisdom bonus, so this one's just "fine".
Magus: Any of the heritages that give a bonus to Intelligence can work very well as a Magus, but unfortunately the race-specific magus Arcana are only available to Seascarred skinwalkers, who get a -2 to Int! WTF, Paizo?! I will instead highly recommend the Scaleheart skinwalker heritage with the Hexcrafter magus archetype, so that you can make use of the Scaleheart-specific hexes, all of which are delightfully creepy and cool.
Monk: With a Wisdom bonus and a floating bonus to a physical score, the vanilla skinwalker is actually really excellent as a monk. Ragebred and Seascarred can also make excellent monks, as can Witchwolves thanks to the Wisdom bonus that they gain when shifted. I also like the Wolf Style line of feats available to Witchwolves, which focuses on slowing enemies and tripping them. Overall, a solid option.
Oracle: Like other Charisma-based casters, the only really good option for you is the Fanglord, and even then you're going to take some penalties to your Charisma-based skill checks when you're in bestial form. Skinwalkers just aren't really meant to fill Charisma-based roles.
Paladin [Antipaladin]: Paladins also use Charisma for many things, but their focus on martial combat means that you can make a skinwalker paladin work more easily than a straight Charisma-caster. I particularly like the Fanglord for a ranged Paladin build, and the Scaleheart or the vanilla skinwalker can both make for good melee-based paladins and antipaladins.
Ranger: Skinwalkers were born to be rangers, and they might be the best possible race to build a switch-hitter ranger thanks to the variable physical ability score bonus, since you can get either a Str or Dex bonus depending on how you want to fight in any given combat. Coldborn, Ragebred, and Seascarred all fit the ranger mold, with Coldborn having some really excellent racial feat options for rangers who want to use the natural weapon combat style.
Rogue [Ninja]: Nightskulks are obviously going to make for excellent rogues or ninjas thanks to their bonus to Stealth in urban environments, Dex bonus, and several fun new rogue talents available to them. Fanglords also fit the bill nicely, especially for a ki-pool focused Ninja. If you're stuck with the vanilla skinwalker, you can still make a very good rogue or ninja build by picking the Dex bonus in bestial form.
Sorcerer: Just like the oracle, the only good option for a Sorcerer is the Fanglord, and it's still not ideal, as a Sorcerer will usually want to act as the party "face" and getting penalties to Charisma-based skills hurts that. Intimidate, for example, would normally be used during combat fairly often, but when you're in combat and in bestial form, you get a penalty to it instead of a bonus! BOO!
Summoner: Summoners can pull off having slightly lower Charisma scores than most other Charisma-casters, since most of their spells are buffs. There's nothing really making summoner a GOOD choice for a skinwalker, though, so this one isn't terribly exciting.
Witch: Bloodmarked, Scaleheart and Nightskulk are all excellent choices for an Int-based caster, and Scalehearts even get several thematic new hexes to choose from, so they're going to make extra-awesome witches. If your GM only allows the vanilla skinwalker, just ignore Int-based casters as an option.
Wizard: For the same reasons as the witch, Bloodmarked, Scaleheart, and Nightskulk are great wizard options, though you don't get any special racial options like witches do. If you're stuck with the vanilla skinwalker, move along, there's nothing to see here.
Don't exist for skinwalkers, unfortunately!
Skinwalkers don't have any Paizo-official archetypes, sadly, but I'd like to take a quick moment to self-promote a little bit...
Skinwalking Shaman (Druid Alternate Class): This is a class near-and-dear to my own heart because I created it! It expands the options for skinwalker druids, allowing for a limited version of wild shape as early as 1st level, and giving you full base attack bonus when using natural attacks, unarmed strikes or improvised weapons, all in exchange for more limited spellcasting that starts at level 4. I highly recommend you check this class out if you like druids and/or shapeshifters!
Magaambyan Arcanist: The Magaambyan Arcanist fits the skinwalker's nature theme well, and it's one of the few arcane classes that gets to pull spells directly from a divine caster's spell list. Of course, you need to be Good-aligned to take this PrC, so keep that in mind.
Mammoth Rider: For a Ragebred barbarian/druid, barbarian/hunter or cavalier, this is the ultimate prestige class, the way to make your animal companion Huge-sized and super powerful at higher levels. If you do have levels of barbarian, make sure to take the Ferocious Beast and Greater Ferocious Beast rage powers to give your steed many benefits that you gain when in rage.
Extra Feature: If you use your bestial shape often (and especially if you're a Fanglord... that see in darkness special ability is absolutely AMAZING) you'll want to pick this feat up at least once during your career.
Fast Change: Great for making the most of your action economy, and I would recommend this feat for any skinwalker, but especially a Barbarian who will want to rage, shift to bestial form, and charge all in the same round.
Bat Shape (Werebat-kin): Being able to turn into a flying creature starting at level 1 is AWESOME, and probably should be toned down, as Paizo's general rule for flight is that you shouldn't get access to it until 4th-5th level. But hey, take advantage of it! You can turn into a bat at level 1!
Bloodmarked Flight (Werebat-kin): This is more along the lines of other feats/abilities that allow flight, and while it's still not a bad feat, you're probably better off just buying potions of fly unless you're in a low-treasure game.
Dire Bat Shape (Werebat-kin): A dire bat really isn't much stronger or better than a regular bat, and having to wait for base attack bonus +3 to get it means this is really only worth grabbing if you're a non-caster who wants to fight while flying and you don't have a mage to cast fly on you.
Bear Hug (Werebear-kin): This feat requires Beartrap Bite, which I also don't like very much, and honestly you'd be better off spending your feat slot on Improved Grapple instead.
Beartrap Bite (Werebear-kin): This feat essentially gives you the grab special feature when you score a critical hit with your bite attack, but of course that will only happen on a natural 20 roll, so don't expect to see the benefit very often. It's probably not worth a feat when you can instead have someone cast lockjaw on you and have grab with every bite attack instead.
Ferocious Loyalty (Werebear-kin): I could see this feat being useful for an inquisitor or hunter, and perhaps for a pair of rogues who work together often. As far as teamwork feats go, this one's pretty decent.
Boar Resilience (Wereboar-kin): This feat, at first glance, seems relatively useless. Unimpaired when exactly at 0 hp? How often do you actually hit exactly 0 hp? Normally a monster will hit you and send you from consciousness directly into the negatives. However, ignoring the Endurance requirement to take the Diehard feat could come in handy for some characters. My only issue with this is that every feat that has Diehard as a prerequisite ALSO has Endurance as a prerequisite, so you can't really get away from taking Endurance eventually if you'd like to take something fun like Deathless Initiate.
Strength of Body (Wereboar-kin): If this feat let you replace your Constitution modifier with Strength for ALL Fortitude saves, I'd say it'd be worth taking, but just once per day really doesn't do it for me.
Swarm Scatter (Wererat-kin): This is a fun and thematic feat, and it's perfect for wererat-kin Inquisitors, gaining a +1 bonus to AC for every ally that surrounds you. However, I do want to point out that TECHNICALLY, you can't gain more than a +1 to your AC from this feat, since Circumstance bonuses don't stack, and this feat doesn't specifically say that the bonuses from multiple allies do stack (though I think it's clear that the intent was to have them stack, so ask your GM about this one before you take it).
Swarm Strike (Wererat-kin): Unlike Swarm Scatter, this feat definitely works as intended, giving you a +1 untyped bonus to attack for every ally that has this feat and is threatening a foe when they provoke an AOO from you. This is a no-brainer for a wererat-kin Inquisitor or Hunter. Make sure to take Combat Reflexes to make as much use of this feat as possible.
Motivating Display (Weretiger-kin): Wow, making Dazzling Display even MORE useful? Sign me up now. This essentially makes you a bard, but you get to use Intimidate to both cause your enemies to be shaken and give your allies morale bonuses to attack rolls and skill checks. It's obviously more useful at low levels than high levels, but still it's a GREAT ability for any weretiger-kin melee character.
Surprising Combatant (Weretiger-kin): This is a strange feat, and the only one I think I've ever seen that references the CR of the current encounter. Basically, you can make a Bluff check, and if you beat the DC you can use that Bluff check as your Initiative, but only for the surprise round? Honestly, not worth a feat for any character in my opinion.
Violent Display (Weretiger-kin): This lets you use Dazzling Diplay as an Immediate action when you confirm a crit or deal sneak damage, which is pretty cool, and can be combined with some other fun demoralizing-focused abilities, like Fearsome Finish. Unfortunately, this feat suffers from the issue of the -4 penalty to Charisma-based checks when in bestial form, which is totally counterintuitive in this case, since looking more like a tiger should definitely make your enemies MORE afraid of you, not less. But, c'est la vie.
Wolf Style (Werewolf-kin): This racial combat style feat gives you a sort of strange but very powerful ability... when you deal at least 10 damage to an enemy during an AOO, its base speed gets reduced, and the amount it's reduced is proportional to the amount of damage you deal.... if you deal enough to reduce them to or below a speed of 0 feet, they fall prone. I could definitely see a werewolf-kin Monk or Brawler wasting their enemies with this, and it only gets better as you continue through the feat chain...
Wolf Trip (Werewolf-kin): Combat maneuver-focused characters are always looking for bonuses to their maneuvers that stack, and this one will give a trip-focused build an untyped +2 to trip maneuvers, which is just amazing. on top of that, when you're using Wolf Style you can also choose which square a creature tripped by you lands in! Wowza!
Wolf Savage (Werewolf-kin): Wow. Once you've knocked an enemy prone (either with a regular trip or with your Wolf Trip feat) and you deal more damage to them, you essentially cast bestow curse on them. That's HUGE! Seriously, for a non-caster, this is crazy powerful. A -4 to attacks, saves, ability checks and skill checks, or a -6(!!!!) to an ability score! And there's no reason that you can't bestow a different type of curse on them every round! Sign me up!