It's different for each genre and game.
Some standards for all games
Fun (entertaining), good/tight controls, and gameplay something that just plays well.
By genre:
Racing SIM:
Car handling, content, realistic cars/tracks, and customization (which embodies GT5 so not making much sense why the scores are what they are)
Kart/arcade racer:
Good track design, unique mechanics, many pluses or minuses to various ways to race IE short cuts, items, etc
Platformers:
Graphics, a big push on controls and camera, and level design/mechanics
RPGs:
Story story story story story, presentation, STORY, battle system, STORY!!, content, and last but not least F$%#ING STORY!!!!!
FPS:
Level design (at least in the past), mechanics, online multiplayer, and replay value since typically they're short.
Action Adventure:
Story, mechanics, graphics, content, and puzzles (probably one of peoples favorites but hardest genre to really cover all bases of what people want)
Might think up some more later or people can add to this as they see fit