For two player games I like a decent amount of chance and/or hidden information to put barrier on analysis and relieve the pressure to play perfectly. I can't abide Chess and other games of its ilk. I gravitate strongly towards wargames because they tend to have tighter designs than a lot of other two player games on the market but there are still a ton of stinkers.
I'm much less tolerant of chance in 3+ player games, especially ones that take ninety minutes or more. I can enjoy a bit of chance in a filler but I prefer the player decisions to drive the play in longer games. Bidding, stock holding, incentive manipulation and emergent alliances are what I primarily look for. I shy away from area control games due to the potential for king-making. An exception to this is that I can play a trick taking game for the hours it takes to determine the strongest player. I just find the experience of flopping cards and chatting to be really enjoyable.
I pretty much hate dice and will tolerate them only as part of an otherwise great design. I prefer cards for chance. Dice are for RPGs.
Maybe it's a phase but I find my tolerance for any sort of engine building to be nonexistent at the moment. It feels like a bunch of faffing about with fiddly bits to accomplish very little. Minutiae goes in, VPs come out. Blech.