Personally depending on the game I usually like a solid story line, but for games not story orientated I like fairy fast gameplay and good weapon balance.
I think one of the most important things in a game are the story line and the characters. Without good characters there's no good story line, but without a good story line there are no good characters. After that comes the graphics. A good example is Mass Effect. The game has awesome characters and the story line extends over 3 titles. (Mass Effect, Mass Effect 2, Mass Effect 3)