For those of you who don't know what they compose, here's a list:
Nobuo Uematsu:
I'm sure everyone on here knows this but Uematsu composed the tunes for the Final Fantasy series, creator of one of the most catchy jingles, (the victory theme in Final Fantasy games) composer of upcoming next gen games Blue Dragon and Lost Odessy and claims to be influenced by Elton John.
Koji Kondo:
Composes the music for Mario and Legend of Zelda. Contender for the most catchy tunes ever created, just listen to the theme tune to Mario and Legend of Zelda.
Kazumi Totaka:
Hides a song in every game he composes for. Track record includes Animal Crossing, Nintendogs, Pikmin 2, Mario Paint, Mario Golf TT, Wave Race 64 and Yoshi's Story.
Yasunori Mitsuda:
Don't know much about this one but he's well known. His tunes are Celtic influenced and he was the original composer for Chrono Trigger. He also composed the music for Deep Labyrinth on DS and although the game wasn't very good, the music was.
Koshiro Yuzo:
Composed the music for the Sonic the Hedgehog games, the Streets of Rage games, The Revenge of the Shinobi, Super Adventure Island and ActRaiser, as well as some not very good games.
So let voting commence (although I think I know who's going to win already)