I enjoy games in proportion to the players' excitement. I'm not particularly skilled with words or pictures, so games like Pictionary and Scrabble (or any number of similar games) aren't my forte, but I'll gladly play them because of who I get to play them with.
Okay, and because I'm really competitive; I loathe losing. My favorite games are those with intense competition that I end up winning.
When it comes to board games, I prefer strategy. I'm an INTJ according to the Meirs-Briggs test, a strategist who loves to determine the best course of action (and verbally best my opponents). I love group games, though I'm usually not picky about what we play; I just like playing games with lots of people, whether intellectual or simply competitive. Favorites include mafia and "four on a couch" (not as bad as it sounds).
This may not count as "games" exactly, but I am muy fond of sports. It doesn't matter if we're playing ultimate frisbee or tackle football, the physicality and exertion of sports is exhilirating.
The key to understanding many of my favorite games is time. I come from a family of 8 siblings, so the games we'd end up playing often had to be short or age-inclusive. Long 2-player games like chess, or complex games like Cranium, weren't popular around our house. The key to a good Winslow family game is still a mystery, but when we find one that works we play it pretty much to death.
Just remember, winning isn't everything. It's the only thing.