I'm more interested in multiplayer. It depends on the genre though, I guess. Single player puzzle games are good (well, if it's a good game anyway). Generally for me though, the multiplayer is where a game lives and dies. Some people like to go through a game as they would a book, for the story, but that ain't my style.
Maybe it's a competitive thing, although I've got no interest in actually beating people. I like to have to either outdo an opponent or solve a problem that's been presented. Proving I can beat the AI at shooting, resource-collecting or whatever is pretty hollow to me.