Level 100 Statistics (see level 5, 50, 100)
He's a great Pokémon in Baton Pass chains since he temporarily blocks Roar and Perish Song with Soundproof and can set up a great deal of moves. Not only that, but he's a great Baton Passer on his own as well, being able to shut down phazers easily. He's really fragile though and can be hard to bring in when playing with standards. Mr. Mime needs to be dealt with immediately and effectively, otherwise he can Calm Minds to something like Manectric which can really hurt.
Calm Minding, Baton Passing Mr. Mime. Being immune to Roar makes him an excellent choice for Baton Passing chains and allows him to contribute Calm Minding to the chain as well. He can block hits with his 120 base Special Defense, giving a Raikou-esque Calm Mind / Substitute feel. This is the Pokémon that makes Baton Passing such a dangerous strategy, since it stops Pokemon with Roar. I usually prefer Encore on here to stop Pokémon from Calm Minding up against you and getting away with it. Barrier is a good choice to make Mr. Mime very hard to take down by both physical and special attacks.
Trick a Choice Band into your opponent, and Torment them so they struggle every other turn. It's a decent strategy. I'd rather stick with the first set, though.
Substitute to block status, Encore and pass the Substitute to another Pokémon capable of causing destruction. Mr. Mime is a wonderful Baton Passer, you see.
Put something to sleep, get a free Substitute or Calm Mind and pass it along or begin to sweep.
Recycle. Pure novelty.
For the Baton Passing sets, you'll want lots of HP and Special Defense. Others may concentrate on Speed and Special Attack.
Checks and Counters
Counters for Mr. Mime are Shiftry and Cacturne with immunity to Psychic and resistance to Thunderbolt. Trick band Grumpig will also beat Mr. Mime. Sharpedo can take Psychics and uses STAB Crunch, but has to watch out for Thunderbolt.