Alright, aside from what Tan said-- I like a story with a lot of choices. Not so many that it's overwhelming, but give me replay ability, different choices, different pathways, and different endings... I like options. I like the fantasy genre a lot. I'm a sucker for a good fantasy world.... I'm also intensely fond of horror, particularly if it's psychological. I like dark humor... I like good battle stories or good puzzle adventures.
I also have a bit of a weakness for--don't laugh--dating sims. No, I'm not "a really lonely guy" (I'm engaged now, actually) but thing is... it's like a different kind of puzzle. I like figuring out the personalities of the characters, what makes them tick, what makes 'em happy or pisses them off...
The thing is, I despise almost every dating sim / romance related game I've played because a lot of them suck. I like the -concept-, but the girls often fall flat / are easy to get... if there's no depth to a character, why should I bother caring about them enough to try to date them? Why would I date an air-head? (Screw, maybe. Date? Hell f*cking naw, man.)
And lastly... I like a challenge.