First off, congrats on your Wobbuffet!
Second off, a few warnings:
- Although Wobbuffet is extremely effective in its job, it is highly predictable and thus, easily countered.
- A high HP stat is a boon, but it also risks the possibility of getting KO'ed by a very strong move (think LO Yveltal: 252+ SpA Life Orb Dark Aura Yveltal Dark Pulse vs. 28 HP / 252+ SpD Wobbuffet: 507-595 (96 - 112.6%) -- 75% chance to OHKO)
- It is extremely weak to passive damage. It gets hit by a status, and you don't have a cleric, it's done for.
Now then for the good stuff: Pokemon Wobbuffet can help out in your team:
- Set-up sweepers. By removing certain key counters of your main sweeper(s) Wobbuffet lets them sweep cleanly, with nary a fear of an opponent.
>Luckily, there are several sweepers that benefit from Wobbuffet's ability to trap, remove, or create setup opportunities. This includes Dragon Dance Rayquaza, Geomancy Xerneas, and Swords Dance Blaziken, which all may find it difficult to gain boosts to sweep on their own. --Smogon.
More threats to Wobbuffet, straight from Smogon:
Ghost-types: Not only can Ghost-types such as Mega Gengar, Giratina-O, and Ghost Arceus hit Wobbuffet for super effective damage, but they can also ignore Counter and most importantly, ignore Shadow Tag, making Wobbuffet ineffective against them.
Dark-types: Most of the Dark-types in the tier, including Dark Arceus, Darkrai, and Yveltal are specially oriented, which is troublesome for Wobbuffet, as they are immune to Mirror Coat, allowing them to hit Wobbuffet for super effective damage without repercussion.
U-turn / Volt Switch: Similar to Ghost-types, Volt Switch users such as Thundurus and Zekrom as well as U-turn users such as Scizor and Genesect can ignore Shadow Tag's mechanics and switch into a Pokemon that can KO Wobbuffet if needed.
Taunt: Most Taunt users in the tier, including Mega Gengar, Mewtwo, and Thundurus, prevent Wobbuffet from using Encore and locking them into a move. However, Wobbuffet can still damage them with Mirror Coat or Counter.
Residual Damage: Because of Wobbuffet's lack of reliable recovery, means of residual damage such as burns, poison, sand, hail, or entry hazards can wear down Wobbuffet very fast, to the point where it can be KOed.
Pursuit Users: Although rare, Pursuit users such as Tyranitar, Aegislash, and Scizor can come in and revenge kill Wobbuffet after it has claimed a victim. Wobbuffet can predict the Pursuit by staying in and retaliating with Counter, but this is a risky situation since most Pursuit users can hit Wobbuffet for other super effective damage too.
Phazing Moves: This situation is uncommon due to the fact that Encore stops Whirlwind and Roar, but Dragon Tail users such as Giratina-O, Groudon, and Palkia can take advantage of being Encored and phaze Wobbuffet out. Afterwards, the opponent can switch as they see fit until Wobbuffet returns again.
Shed Shell: Shed Shell users such as Blissey can also ignore Shadow Tag and therefore switch out with impunity. However, Pokemon that use Shed Shell are rare, making this situation very uncommon.
So yeah, these are the thing that you should try to remember and counter.