I host a bi-monthly game night in my home. Each session we compete for the coveted "Sheep Trophy", which spends a lot of time in other people's homes.
I have the most fun playing games that:
1. Are of light/medium complexity. My tolerance for fiddly rules and lots of bookkeeping is very low. I'm easily confused (I like to blame it on aging but it's probably that I'm just not that smart). If it starts to feel like I'm balancing my checkbook or doing my taxes, I'm not gonna like it. I don't mind complexity in games, but I feel that the complexity should arise naturally from the interaction of a few simple rules.
2. Have a high degree of player interaction. I'd much rather be negotiating, attacking or screwing someone over than staring at my own "player mat" trying to figure out how to maximize something. "Spreadsheet" games aren't really my thing.
3. Have mechanics that are closely tied to the theme. I'm into the immersion thing.
4. Are conducive to trash talking.
All that said - to me, its more about the people I'm playing with than the game itself. I'd rather play a game I'm not crazy about with my friends than play one of my favorites with people I don't really like.