I like it when the stories are believable, as others said. Characters that have more dimension to them helps, but good descriptions and a host of tertiary characters make it more believable. I've noticed that of the stories I really like, there are maybe 1-4 main characters, 2-6 supporting secondary characters, but then dozens of named and unnamed tertiary characters to fill it up. Even something as simple as, "Emily kept getting bumped in the hallway so was late to class and had a hard time finding her seat in the crowded lecture hall," is much more satisfying to me than, "Emily walked to class and sat down, almost arriving late."
It's something I'm working on in my own writing, and it's something I need to go back and add, I think.
I also like stories that are paced well, which is hard (I personally think my stories are too slow moving). You need time to build sympathy for your main character(s) and turn them into "real" people for the reader, but at the same time, 5 chapters in a row about how they woke up, went to work, out to lunch, back to work, made dinner, and then went to bed is just boring. Yes, you get to know the character and may be more inclined to sympathize with them when they get into trouble, but you want to kill the author.