Here's what I like in games:
Games with a story or definite goals, something I can beat 100% and know I've done everything. I don't like completely open-ended things or games that are mostly online multiplayer battles. RPG's, action/adventure, campaign mode in TBS/RTS, platformers with lots of collectibles, etc. Sometimes I can get into season mode of sports games.
As far as simplicity vs. complexity, I might agree that I prefer a game that I can actually start playing after an hour or two and feel like I'm actually progressing. I never understood the appeal of memorizing 500-button combos for Virtua Fighter or whatever those fighters do. But to name something like Final Fantasy as complex just destroys the point, they're deep and long but they're hardly difficult. If you want something hard play some old NES games, most of those are insane.
