In past Pokemon games I really haven't found any real reason to use Mr. Mime. BUT seeing as I started with Charmander, but deposited him because of EV's and his Blast Burn move. I found trading that level 8 Abra for this Mime was one of the best things I have ever done. He has been absolutelly awesome for in-game, but my question doesn't have to do with tournament or serious play.
In FRLG he is able to learn Magical Leaf at level 22, and seeing as he was traded it's not hard to get him to that level. He was crucial to me gettin through all of Rock Tunnel (and all those durn Hikers with Geodudes) plus he learned Flash. With his Soundproof ability he doesn't get hit by Sing, Growl, Snore (Snorlax wasn't hard to catch at all b/c of this and Substitute btw...), Supersonic and other sound related moves, he lets the stupid AI waste crucial turns. Plus his Substitute can protect him from any special condition, which is great against the Gym Leaders that thrive on that fact. He just absolutelly shredded Erika's pokes (half psn), Koga's are all psn (+ Toxic = no good against sub), Team Rocket hasn't posed any threat at all (Game Corner, Silph Co., and Pokemon Tower) w/his Psybeam/turned into Psychic. Because I started with Charmander my Rival's Squirtle (Evo's) haven't been a problem at all.
I just can't believe how quickly this Pokemon has turned from one of my last choices for an in-game team to the automatic must have for any play-thru of the game. He doesn't even require any TM's to be good. I've even kept Flash on him, and I'm cruisin along fine with: <>Psychic<>Substitute<>Magical Leaf<>Flash<>
What do you think?