If by rule you mean have better than the 360 but ignore the Wii, DS and PSP then maybe.
lets see what we have when we don't play silly buggers (in all cases considering games that we know are in development, or already released. Not considering VC, WW, XBLA, PSN)
Action Adventure - All home consoles are on about equal footing. I would give the award to the Wii, but I recognise that that is just my opinion. I just don't see how he titles you mentioned can hold a candle to two Zelda games (1 released 1 unreleased) and 4 Metroid games (3 released 1 unreleased)
platformer isn't as big as it once was? The sales of mario games beg to differ my friend. Wii>DS>>>>>>>>>>>PS360+PSP combined
Racing - this isn't a genre.
Driving simulators - PS3 wins here cos it has GT5 coming soonish
Offroad racers - I'm not really sure, the last time I played this genre was the Dakar game on the 'cube.
Kart racers - Wii>DS>>>>>>>>>>>PS360+PSP combined, due to mario kart
FPS - If you priritise graphics and online gameplay it's
360>PS3>Wii>PSP>DS
If you priritise controls and local gameplay it's
Wii>360>PS3>DSi>PSP
RPG
DS>>>>>>>>>>>>>>>>>>>>>>PSP=Wii>PS3=360. Although I predict by the end of the gen Wii will be much better than PSP
Fighter
Depends if you like Brawl or not







