The one and only set for Wobbuffet. With little prediction, or none at all if Encore is used, Wobbuffet can guarantee at least one kill against a Choiced Pokemon (preferably a Pokemon with Choice Scarf). Choose Counter if your opponent is clearly a Choiced physical attacker, or Mirror Coat if it's a Choiced special attacker. If it's a Pokemon without a Choice item, simply use Encore and proceed from there since your opponent can't switch out. Encore can also work to your benefit if the opponent chooses to use a stat up move, as this will allow a free switch in for one of your Pokemon and at least one turn of set up. Encore is especially effective against defensive Pokemon, such as Lugia and Blissey, as the best they can do is use Toxic on Wobbuffet, and the move is rare on Lugia. Forcing a Pokemon to repeat a move while preventing them from switching is one of the most sadistic, and effective, strategies in Pokemon. Wobbuffet can also switch into a lead Choice Scarf Darkrai's Dark Void, forcing it to struggle to death. This can be risky, because if Darkrai uses Trick, Wobbuffet is crippled, and if Darkrai uses Dark Pulse, then Wobbuffet will take a massive amount of damage (and it cannot use Mirror Coat, as Darkrai is immune to it).
Both Safeguard and Destiny Bond will be helpful as your last move. Safeguard is obviously there to prevent Wobbuffet from being crippled by status ailments and can help it support the team at the same time. The only downside is that Wobbuffet is very slow and will most likely be statused before it can use Safeguard. Still, Encoring a status move and using Safeguard can be an effective way to set up a sweeper. With Tickle, Wobbuffet can become an effective wallbreaker when paired with a user of Pursuit (such as Tyranitar or Scizor). Destiny Bond is a good option that should be used alongside Custap Berry to pick up a KO when Wobbuffet is weakened, but forfeiting Safeguard and Leftovers recovery is usually not desirable. Tickle is an incredibly niche option; Tickle Wobbuffet's main targets are Lugia and Blissey. Once Lugia is Tickled and Pursuited to death, most stall teams will be vulnerable to sweeps from deadly physical setup sweepers, like Rayquaza or Garchomp.
The given EVs are fairly obvious, since Wobbuffet has a massive base HP stat and poor defenses. The 28 HP EVs allow Wobbuffet to gain maximum Leftovers recovery and, with a Calm nature, allows it to survive a Modest Kyogre's full powered Water Spout and OHKO back with Mirror Coat. Calm is emphasized over Bold because of the concentration on special attackers in Ubers; however, Bold can be useful to better handle Groudon, Rayquaza, Garchomp, and other physical threats in the Uber metagame.
Thanks to Wobbuffet's ability, Shadow Tag, Wobbuffet is hard to stop. However, Wobbuffet is most vulnerable after a revenge kill. After a revenge kill, Darkrai can easily switch in and ether set up on Wobbuffet by using Taunt or outright kill it with Dark Pulse. Mewtwo can also Taunt Wobbuffet and set up Calm Mind as a result. Because of this, Choice Scarf Heracross can be a useful Pokemon to pair with Wobbuffet, as Heracross can force both Darkrai and Mewtwo out, thanks to its STAB super effective Megahorn. Choice Specs Kyogre can also switch in on Wobbuffet after a revenge kill, so having a Pokemon who can survive Kyogre's Water Spout and scare it off is important. Latias is a good choice for scaring off Kyogre, because despite Water Spout 2HKOing Latias, Latias can use Thunder or Grass Knot before Kyogre can move, thus weakening the Base Power of its Water Spout. Palkia is a good choice as well, because Palkia takes less from Water Spout than Latias, at the cost of no recovery move.
The secret to Wobbuffet's success is to use Pokemon who work well with him. Rayquaza is an excellent Pokemon to pair with Wobbuffet for a number of reasons. Wobbuffet can easily revenge kill Choice Scarf Dialga via Mirror Coat, which is many teams' best hope of stopping Swords Dance Rayquaza. Wobbuffet also helps out Dragon Dance Rayquaza by destroying its primary revenge killers, Choice Scarf Palkia and Choice Scarf Garchomp. Wobbuffet can also destroy Lugia via Tickle plus a Pursuit user, such as Tyranitar or Scizor, which greatly aids Rayquaza's attempts to sweep stall teams. Lucario also works in a similar manner to Rayquaza, but Lucario makes up for its weaker offenses with a typing that covers Wobbuffet's weaknesses. Lucario resists Ghost-type attacks and has a 4x resistance to Dark- and Bug-type, all of which are types to which Wobbuffet has a weakness.
One of Wobbuffet's main weaknesses is that it can often only revenge kill one Pokemon per match, thanks to its lack of a recovery move; thus Wish support can greatly aid Wobbuffet. The main users of Wish in Ubers are Blissey, Jirachi, and Latias. Jirachi has the benefit of being able to Wish and then U-turn right back to Wobbuffet. Jirachi is very vulnerable to Groudon though, so it is best if you eliminate Groudon by U-turning on the switch, and bring in a powerful special attacker, such as Kyogre. Blissey and Latias are also viable Wishers; however, both are vulnerable to Scizor, a Pokemon who Wobbuffet often has trouble with as well, so only use those two if Jirachi cannot fit in your team. Blissey can also provide Aromatherapy support for Wobbuffet, which can be useful, but is risky because the opponent can easily send in a physical sweeper or an opposing Wobbuffet to set up on Blissey.
Wobbuffet has problems with powerful Choiced Pokemon, such as Choice Specs Kyogre and Choice Band Groudon, as they can easily OHKO or do a severe amount of damage to Wobbuffet. Because of this, Pokemon who can use Light Screen and Reflect can help Wobbuffet take the powerful attacks of Ubers much more easily. The prime Pokemon for the job are Mewtwo and Deoxys-S. Deoxys-S can make a good lead, and thanks to Taunt and its massive base 180 Speed stat, Deoxys-S can shut down attempts to Taunt it. Deoxys-S can then proceed to use Light Screen and Reflect. If Deoxys-S is not a good lead for your team, then Mewtwo is the better choice, as Mewtwo can use Self-Destruct after it sets up Reflect and Light Screen.
If you are using Tickle on Wobbuffet, there are two main Pursuit users to consider: Tyranitar and Scizor. After Tickling Lugia or neutral natured 4 HP/252 Def Blissey two times, a neutral natured Tyranitar with 56 Attack EVs and a Choice Band will OHKO either of them while they switch. Adamant Scizor with Life Orb and 100 Attack EVs requires a switching Lugia to be Tickled five times and Blissey to be Tickled four times to OHKO them with Pursuit. This can also work with Giratina, but Giratina must lack Will-O-Wisp, or else Giratina can burn the Pursuit-user and live. An Impish 248 HP / 248 Defense Giratina must be Tickled five times for a 87% chance of Scizor's Pursuit to KO on the switch, and three Tickles for Tyranitar to KO. While Tyranitar requires less Tickles to KO these walls, Scizor is not affected by Toxic, which Blissey or Lugia may use on Wobbuffet. While it may be tempting to use less Tickles so the walls will be KOed by the next switch in to Stealth Rock, this is not recommended because a common Pokemon on Uber stall teams, Forretress, can easily use Rapid Spin to get rid of Stealth Rock.
In general, any setup sweeper will enjoy support from Wobbuffet, but Wobbuffet is especially effective with users of Substitute. For example, Wobbuffet can Encore a support move from a Pokemon like support Groudon, and send in Darkrai. Darkrai can then Substitute, and scout out the opponent's team. If the opponent sends in a Pokemon who ends up breaking your Substitute before you move, then it is evident that it has a Choice Scarf, and you can then send in the appropriate counter or revenge kill the Pokemon later with Wobbuffet. This strategy is also effective for setting up SubSeeders, such as Jumpluff and Shaymin-S. Another strategy to employ is abusing Thunder Wave. Since Wobbuffet will be faster than any paralyzed Pokemon under a Speed stat of 408, Wobbuffet can easily switch in on a weak move (such as Mewtwo's Aura Sphere), Encore, and then proceed to KO the paralyzed target.