Gens 1 and 2
Both Sandslash formes now have access to Spikes. However, it's hard to say they'll be successful Spike setters due to freely inviting common Defoggers in Corviknight and Skarmory while simultaneously being unable to threaten them at all.
Wigglytuff, like Clefable, can now run Teleport + Wish. However, there is a strong chance that Clefable will naturally outclass it for a few reasons. Clefable has Magic Guard, which is a huge advantage over Wigglytuff since it prevents Clefable from having to heal itself from chip damage that's normally taken from status and hazards. Clefable being a pure Fairy-type also allows it to resist Fighting-type attacks, which may prove to be useful now that the tier has new Fighting-type threats in Urshifu and Heracross.
Unfortunately, Golduck only got Muddy Water and Flip Turn. There was no reason to use it before, and sadly it looks like that won't change.
Poliwrath got a ton of new moves with Drain Punch, Reversal, Superpower, Muddy Water, Close Combat, Darkest Lariat, High Horsepower, and Liquidation. It already had access to Belly Drum and it does have the Swift Swim ability, so it finally has potential to be used on Rain. However, it doesn't have the highest attack stat, which may result in disappointing damage output. For example, a +6 Jolly Poliwrath only does 58.8-69.4% to Toxapex in the rain with Liquidation, which may ultimately force it to run Earthquake solely for Toxapex. There's also some new bulky water and grass types in Slowbro and Amoonguss that may give Poliwrath trouble.
Alakazam may turn out to be a very strong special threat in OU thanks to having gained Nasty Plot this generation. It sits at a very nice speed tier, which allows it to outspeed everything except for Talonflame, Weavile, Dragapult and Zeraora. While Alakazam got Nasty Plot, it also has to deal with Chansey, Magearna, Aegislash and Mandibuzz. Chansey is an interesting interaction because if Chansey opts to run Toxic over Thunder Wave, then at best, it has to spam Seismic Toss vs. Alakazam to threaten it (it does 39.8%). In return, after a single Nasty Plot, Alakazam's Psyshock will always 2HKO Chansey (the roll is 50.7-59.7%). While Chansey may not be a huge problem for Alakazam, Magearna could potentially stop Alakazam. In addition to resisting Psychic-type attacks, Magearna has options to boost its own stats with Calm Mind, and could KO with moves like Iron Head. On the other hand, +2 Focus Blast from Alakazam has a high chance to 2HKO Magearna, after Stealth Rock, so it's not a perfect answer. Aegislash is able to tank hits from an Alakazam that opted to run Recover in the 4th slot over another coverage move. Aegislash can tank a hit and threaten back with Shadow Sneak. Mandibuzz is similar to Magearna where it doesn't care about Psychic-type attacks and mainly has to worry about Focus Blast. However, unlike Magearna, Mandibuzz can 1HKO Alakazam with Knock Off (Foul Play will fail to 1HKO if Alakazam runs 0 IV's in attack). Overall, I think it has pretty good potential and should be an exciting addition to the metagame.
Tentacruel I personally don't think will stay in OU for a number of reasons. Unlike other defensive hazard removers (Skarmory, Corviknight, Mandibuzz), Tentacruel has no recovery options outside of Leftovers. You could make the same argument about Excadrill, but Excadrill was also used for offense, which is something Tentacruel won't be used for.
Slowbro finally gives us another bulky Water-type. It can reliably switch into a lot of physical attackers, most notably Excadrill and Cinderace. It gained a lot of new moves, including Imprison, Weather Ball, Mud Shot, Psychic Terrain, Hydro Pump, Stored Power, Liquidation, Expanding Force, Razor Shell, Muddy Water, Nasty Plot and Body Press. It's also important to remember it has access to Teleport now, which can allow it to grab momentum after switching into a mon it checks.
Regular Exeggutor gets access to Calm Mind now, but it unfortunately did not get Weather Ball. It's hard to say if it'll have any success in OU if it has zero options on the special attacking side to deal with Steel-types.
Alolan Exeggutor got Power Whip and not much more. It has some nice coverage options in Flamethrower and Earthquake, but it's very slow and not too powerful, so it most likely won't be seeing any usage in OU.
Marowak didn't get anything notable and although it hits pretty hard, it won't appreciate having to deal with Corviknight and Tangrowth.
Alolan Marowak on the other hand actually got Poltergeist. I'm not sure if Poltergeist will end up more consistent than Shadow Bone, but it's a nice option that can help it deal more damage. Alolan Marowak should be nice for Trick Room teams and is a pretty scary threat in general due to its amazing coverage in Ghost + Fire + Ground attacks.
The fattest pink blob has returned to wall every special threat in the book. A lot of pre-dlc mons such as Kyurem, Hydreigon and Dragapult were able to be as good as they were because Chansey was gone, but now that Chansey is back, it'll be interesting to see how those mons perform.
Kangaskhan didn't get anything special either, so it's probably not going to see any usage.
Starmie gets Agility and it has access to Teleport. Teleport is pretty cool and could allow Starmie to use a moveset of Rapid Spin + Recover + Scald Teleport to play more of a utility role. The major flaw with this however is that it's hard to justify the purpose in running Starmie in the first place. In other words, if there isn't anything common that it can check, then there's not much reason using it.
Scyther gets a few new moves in Assurance, Psycho Cut, Cross Poison, Acrobatics, and Dual Wingbeat. It gets the Technician boost for Dual Wingbeat and has the option to run Heavy-Duty Boots now. However, it doesn't really have good coverage options to help break through common physically defensive mons like Toxapex and Corviknight, which ultimately means it's gonna struggle too much.
Pinsir got Reversal and High Horsepower, but without mega evolution, it's not worth running.
Tauros got some cool moves including Assurance, Revenge, Reversal, Megahorn, Close Combat, High Horsepower, Throat Chop, and Lash Out. Unfortunately it still lacks any boosting moves, or moves to boost its stats, meaning that it will struggle against common physically defensive threats like Hippowdon.
Although Azumarill didn't really gain any notable moves (it gained Brutal Swing, Mud Shot, Draining Kiss, Misty Terrain, Misty Explosion, and Steel Roller), Azumarill does add a great Water-type wallbreaker to the SS OU roster. With Belly Drum and Huge Power, Azumarill is the kind of Pokemon that can quickly snowball out of control. Azumarill lacks much of any consistent defensive counterplay, but it is still held back by faster Pokemon that resist Aqua Jet such as Kyurem, and the fact that it can sometimes struggle to find opportunities to set up if pressured enough.
Politoed has access to some new moves, most notably Weather Ball and Earth Power. Pelipper existing gives it a tough time and it will probably remain outclassed by Pelipper like it did last generation.
Slowking doesn't have as many useful new moves like Slowbro does, but it still has access to Teleport and now learns Weather Ball. I don't think it'll use Weather Ball, but like Slowbro, it should be nice to have Slowking grab momentum with Teleport after switching in to check an offensive threat.
Dunsparce already had an insane move pool to begin with, but now it has access to Helping Hand, Amnesia, Baton Pass, Stored Power, Terrain Pulse, Dual Wingbeat, Skitter Smack, and Scale Shot. It's stats hold it back a lot, and that sadly won't change this generation either.
Scizor is most notable in SS OU for the defensive utility that it brings with it; it is an excellent check to Pokemon like Kyurem, while also being capable of pressuring Pokemon like Clefable. Unfortunately, Scizor didn't really gain any new tools it can make use of besides Psycho Cut, which it can maybe make use of to pressure Toxapex more consistently.
Heracross notably gained access to Spikes, which can make it much easier to wear down defensive mons like Hippowdon and Kommo as well as faster mons like Dragapult. Spikes also gives it a tool that sets it apart from Urshifu and Conkeldurr as a Fighting-type wallbreaker. Considering its pretty good matchup against entry hazard removers like Corviknight and Mandibuzz, this could be very useful.
Skarmory only gained 4 new moves: Wing Attack, Sand Tomb, Body Press, Dual Wingbeat. Body Press is pretty interesting as it allows Skarmory to directly pressure mons like Excadrill and Magnezone with damage instead of needing to rely on Whirlwind. Skarmory also gives us another Excadrill counter and should help deal with some of the new physical attackers in the tier.
Kingdra has finally gained access to Hurricane, which is a fairly big change because it would struggle to break through specially defensive Grass-types like Amoonguss and Assault Vest Tangrowth in previous generations. Kingdra is looking to bring a lot of new tools to rain teams; being a very fast Swift Swim user with some pretty useful utility as a Water / Dragon type.
Porygon2 gained a few mediocre/useless moves in Thunder Shock, Power Swap, Guard Swap, Speed Swap, Eerie Impulse. It does have Teleport, but it's a little hard to justify using it in the first place when Chansey exists.
Miltank now gets Play Rough, Charm, High Horsepower, Heavy Slam, Body Press, Steel Roller. Defensively it faces a lot of competition with mons like Hippowdon and Corviknight, and then offensively, it's outclassed by Snorlax as a Curse user.
Blissey gets Life Dew and Stored Power. I know some people talked about Calm Mind sets in the previous thread, but I'm personally not too sure how they'll turn out to be. Chansey should outclass it as a utility/support mon, but it'll be interesting to see if someone finds a use for Blissey.