Western RPGs mostly. I prefer well paced, deep story-based linear RPGs with a focus on strategic battles like the Baldur's gate series, Planescape Torment, Gothic I and II, Betrayal at Krondor back in the day etc. Dragon age was decent too but the Baldur's gate series was the pinnacle or RPGs for me, it's been downhill from there gameplay and story wise, even when the graphics are always improving.
I always try but never get very far into mainstream hack and slash grindfest RPGs like Diablo or huge sprawling RPGs with very little story and little point to the endless grinding, like the Elder Scroll games, no matter how pretty the graphics. Most people seem to enjoy them like crazy though.
Also big into the Story driven Puzzle / Adventure genre but those seem to be fading out lately. Was big into the old school Sierra and LucasArts point and clicks back in the day.
Also enjoy some strategy, usually whichever latest Civilization game is out although 5 was a step back IMO.
I'm also on Osmium's page in that I feel like most gaming genres I enjoy have started to suck lately. Online games are the worst, as they're too dumbed down and catering to the rich stupid demographic that will pay $50 for every new weapon and shiny purple umbrella in the game.
I actually worked in game development for a pretty famous MMO game company for a while and have done a bit of indie game dev myself.