I'm going to be a contrarian. I like the starship combat system.
- It's easy to learn;
- it includes all players equally;
- it lets all character types participate;
- it encourages (requires) teamwork more than even regular combat;
- it raises the stakes of the game.
I don't think it's perfect and is most fun in relatively small doses, but people generally seem to have fun with it in my games.
My favorite part (like many of you) is the setting. Least favorite... honestly, the supernova of weapon and armor types is a little too much to keep track of. But then again, too many options is a pretty good problem for a game system to have.