It's pretty obvious that the answer is the xbox 360. It has the most games and has massive 3rd party support; something that the other 2 systems don't have. The Wii has a lot of games, but only the ones produced by Nintendo are any good. Th PS3 just has a weak line up all around. What the PS3 does have is a lot of "potential", so the fanboys say; the proof is in the sales. The 360 is targeted at the average gamer so that include an array of titles of all kinds.
FPS: Halo 3, Gears, Bioshock and so on.
RPG: Eternal Sonata, Blue Dragon, and soon to be Star Ocean and Tales of Vespa
My personal favorite, Fighting: DoA 4, Virtual Fighter 5, Burst Limit
Adventure: Ninja Gaiden II, Iron Man
Sports: all kinds but I don't play them lol