Gameplay because I want to play a game in which I can do many stuff, not a game in which I go right forever, or repeat the same thing forever.
Story because I am not really sure if I want a game with STORY or not, but either way, one point because it does matter, not much for me because sometimes I want to play the GAME, not the STORY.
Graphics because forget. Minecraft has perfect graphics, BF3 has perfect graphics (but I don't have it
). Either way, the points goes not for the quality, but how the graphics fit with the game.
Music because sometimes music ruins the game. In Just Cause 2 when I just drive around nicely I don't want to hear battle music, or in other games. Some games don't even have music to give more concentration.
Difficulty because I don't really want to be God all the time, but I also don't want to repeat the same thing 10 times till I get it right.
Voices because player-player interaction in singleplayer is not.. logical, but playing alone makes me sad, so character's voices make me happy (hurr durr).
Realism on realistic games, fantasy on fantasy games. What I mean with realism here is about the things working correctly, environment, having the feeling I am there, etc.
Replayability: I hate linear games most of the times, if I pay money for a game I want to play it for more than 1 day. I hate stuff that have linear gameplay that you can't really play 'normally' after (only story mode).
Controls: There usually is a way to set my own controls, if not, someone out there made an mod to do so anyway.