It depends on what I want out of a certain genre, and what is promised of that specific game. It could be any number of things.
For example, when Bioshock came out, I was told the story was superb and the gameplay was lacking. I agree.
Counter-Strike is supposed to be a skill based FPS consisting of only multiplayer. And it is.
Or I'm playing a platformer, such as Super Meat Boy, I expect to be challenged. I expect to have to have good timing, to have good depth perception, or to be able to judge distance.
I guess you can say what makes a game good for me is the game executing what it set out to do originally.