Im gonna go with immersion..
If I can feel like Im in the game, it's got to be a good one. This naturally means that there cant be anything that reminds me that it's a video game, such as noticeable bugs, poor writing/story or just gameplay so bad or boring I keep noticing it. Graphics, however, dont seem to be such a big factor. I mean, Limbo was really immersive for a 2D puzzle platformer, for example.
Atmosphere can bring an average game to unexpected heights.
EDIT: This doesnt mean it has to be first person, though.. Arkham Asylum was incredibly immersive, for example.