Hmm...*looks at own username*
I love games that simulate things that due to lack of money, skills, or time I don't get to do in real life. Besides the obvious MS Flight Sim (which I play, but not nearly on the enthusiast level of some virtual pilots), I'm a particularly big fan of business/tycoon-type sims and city builders. I love anything that I myself create when it comes to video games, and the more of a sense I have that I built/tweaked/recruited whatever's on the screen, the more personally involved and immersed I become.
I buy a new sports game only after I've beaten the last one absolutely to death and run up against the limits of its franchise mode (most football and basketball games seem to cap at 30 seasons). By the time I'm into Year 5 or 6 (in a pro game) or Year 3 (in a college game), just about everyone in the lineup has no real-life counterpart because they were generated by the game's rookie draft.
I find pre-manufactured characters and settings dull. I think Grand Theft Auto 3 is the series' best game mostly because your character is what you make of him; it's the most wide-open game of them all and leaves the most to the player's imagination. Morrowind and Oblivion fall into this category as well; that character I'm controlling isn't some story writer's (or worse, marketing executive's) idea of what I should be (which is one reason I really don't like JRPGs), but rather it is a character whose motives and desires are mine and mine alone.