Wobbuffet is banned for two reasons. The first is that the generally accepted definition of a counter is that you can switch in a Pokémon and then defeat or scare off the enemy, and Wobbuffet prevents anything from switching in. The second is that Wobbuffet vs. Wobbuffet will not end if they are holding Leftovers, because Leftovers heals more than Wobbuffet can hit with Struggle. However, it can be a powerful Pokémon to set up a Belly Drum sweeper if you Encore a non-attacking move.
Switch it in or lead with it (you want this to take as little damage as possible before it's actually in, as taking damage is needed once it's there), and then Encore. If they attacked you, kill them. If they used a stat increasing move such as Calm Mind, take the free switch to any Pokémon you like and own them with it. If they use a status move, then Safeguard first, or, for loads of fun, pair with a Choice Band Facade Swellow; Encore status, switch to Swellow, OHKO everything. If they are using Choice Band, then you don't even need to bother with Encore. Though, if your opponent might be using Wobbuffet don't use Choice Band, except maybe on Heracross. Use Lum Berry or Focus Band if you suspect your opponent is using a Wobbuffet, too, as this will allow the Struggle war to end, so you can use this to switch to a Smeargle or whatever after they kill your Wobbuffet, and they'll have a completely useless Pokémon getting in the way. Some competitive events that allow Wobbuffet ban it from holding Leftovers to prevent Wobbuffet vs. Wobbuffet from lasting forever.
Destiny Bond has a very limited use on Wobbuffet. Wobbuffet is too slow to Destiny Bond on anything but Snorlax, so the main purpose would be to kill Dark Pokémon that are using special attacks or Ghost Pokémon using physical attacks. Tickle could be used to try and weaken an enemy's attack, to set up an unbreakable Substitute for a Bellyzard or something. Tickle also allows Wobbuffet vs. Wobbuffet to end, and it ends in the Tickle user's favor, just not in the way you might think. Tickle has less PP than Safeguard, so the Tickle user will run out of PP first, and thus die to Counter with Struggle. This is actually a good thing, because you still get a free turn vs. a Pokémon that is guaranteed to do nothing, unless you have 1 HP and don't kill it.
252 Defense, 252 Special Defense and Careful / Impish. You get better defenses this way than by adding HP. Even though you'll do slightly less damage with Counter and Mirror Coat, it's better to survive the hit and Counter than die and not Counter, and you'll still OHKO most heavy hitters, and 2HKO most of the rest.
Checks and Counters
By definition a counter has to be able to switch in, and nothing can switch in. However, notable mentions are Toxic Dugtrio / Gardevoir / Porygon2, as they trap the enemy Wobbuffet. An even better option is Calm Mind Gardevoir. Rather than simply killing Wobbuffet, the Gardevoir user can sacrifice a Pokémon, come in, Trace Shadow Tag (thus trapping Wobbuffet), and use Calm Mind 6 times. Your last move should be Substitute. Kill Wobbuffet with Ice Punch, and tell your opponent good luck, because they'll need it to stop 6x Calm Minded Gardevoir behind a Substitute. Sharpen / Agility Porygon2 works in the same manner.
Wish makes Wobbuffet even cheaper. Wobbuffet's effectiveness increases exponentially with Pokémon that can set up. An old strategy that pops up every once in a while is that Wobbuffet Encores a Shadow Ball or set up move, switch to Smeargle, use Substitute, Belly Drum, and pass to Rayquaza / Medicham. Wobbuffet can also work with Perish Trappers in 2v2. You get the automatic Mean Look, so all your partner has to do is Perish Song, and maybe Torment while Wobbuffet Encores, making it unable to hit you with any attack other than Struggle.