I like games which are mechanically quite simple but tactically quite deep. I dislike games which plough extortionate amounts into making things complicated just to get very minor gains in the tactical depth of the game.
Genre wise I like Investment games, other economic games, war games, worker placements, dice games, card games, area control games, civilisation building games and some co-ops (but ONLY hidden traitor/hidden personality type games)... anything can take my fancy if it's mechanics are nice. Only things I'm not keen on are Role playing games, CCGs, the new 8th edition warhammer rules, Citadels company policies and warhammer opponents who get a bit too 'in character'.
For me an absolutely perfect game is one which forces me to think hard in every single turn and re-evaluate based on others moves, yet one which I could just as easily slap down on the kitchen table and have a good game with my mum/gf/brother.