Since everyone's making lists, I'll make my own lol.
Action/Adventure - Easily the Wii! Between Twilight Princess and Okami (okay, they're not exactly exclusive, but they're close enough) and other titles, the Wii comes out on top. Trico will be the only decent competition from the other camps for these titles, but Nintendo always has another Zelda up their sleeve, so I can't see them losing the crown.
Hack n' Slash (because I don't think games like God of War fit in with games like Zelda) - The ps3 wins here, with Heavenly Sword and Ninja Gaiden Sigma, plus God of War III (the mother of them all, imo) and Ninja Gaiden Sigma 2 on the way.
Platformer - My vote goes to the ps3, because LittleBigPlanet is an absolute blast, and is probably my favorite game this gen. And it has 750k levels and counting (of which at least ~100 or so are pretty good, from my own personal experience). Plus, the ps3 has the pseudo-platforming series Ratchet & Clank. The Wii comes very, very close, though, with Super Mario Galaxy and Super Paper Mario.
Racing - I'm not really into sim racers (well, most racers, really), and racing series I really play is Mario Kart, so the Wii gets my vote here. Plus playing with the wheel is just awesome. I'd say the ps3 would take second place, though, because of Gran Turismo, MotorStorm, and Wipeout. 360 is a close third with Forza and PGR.
Shooter (no, I'm not limiting this genre to just FPS) - I'd say it's almost a tie between the ps3 and 360, with the nod going to the 360. In my opinion, Killzone 2 > Gears of War 1/2 >>> Halo 3 >>> Resistance 1/2. But I'm a bit biased against Halo and Resistance, since I like my shooters a bit slower and more tactical. There's also the issue of what genre MGS4 resides in. This could tip the scale back in favor of the ps3. The only description that fits for the game, imo, is Tactical Espionage Action. :P
RPG - At this point, I'd say it easily goes to 360. It has Mass Effect, Lost Odyssey, Blue Dragon, and a few others to call its own. Of course, if games keep going multiplat (Star Ocean?), that could change. I would say the ps3 comes in second, but sadly its best RPG (Demon's Souls) has only been released in Japan and Asia, so that doesn't really count. The Wii is certainly picking up steam too, with titles like Arc Rise Fantasia soon to be released, and Tales of Graces and Monster Hunter 3 in the future.
Fighter (I like how he just ignored this one lol) - Easily Wii! SSBB > all other fighters this gen. Everything else of note is multiplat ps3/360, so they tie for second.
And yes, I ignored the handhelds.