I can play pretty much anything that's not racing, sports or Tom Clancy though I often decide on a case by case basis for no real reason. RPGs only occassionally since they take way more time than I have so I forget about playing them further (I forget faster if the RPG is open-ended). 3d fighting games not much as I can't remember arbitrary button sequences well and prefer the direct mapping of 2d games where a button tends to do the same thing every time and I can remember my combos by action instead of button. Not sure about platformers, haven't played many of those. I like sidescrolling 2d games but that probably doesn't do anything on home consoles. I prefer FPSes with lots of firepower and targets, going out and killing stuff instead of cowering behind a wall and emptying a whole clip into a single target. I've made the experience that great games of a genre tend to be fun even for those who don't know or like the genre though.
Overall I'm looking for good games I can't get on my PC or Wii though. I guess the difficulty of putting what I want into words is also the reason I have trouble finding a game selection.