In general:

Replay value > Music > Graphics > Multiplayer

Storyline is typically linked to replay value in such games where it is important. A good story is either interesting enough to be experienced again (if not skipped outright), or follows a branching path and functions as an incentive to play through the game a second time. If the story and pacing aren't good, chances are the game isn't either.

Replay for me. Though story is close. As is Multiplayer... but by Multiplayer i mean co-op. Co-op won't make me not buy a great game... but it will make me buy a good or ok game.

Really i'd go

Replay-Multiplayer(co-op)-Storyline-Multiplayer(Vs)- Audio - Graphics.

The more i think about it, the more i realize the right music sets up parts of a game better then graphics do. That's what used to be great about the old squaresoft RPGs.  It has some songs that i'd want to listen too while not playing the game.

storyline

Replay value, I don't want to buy a game just for 6 hours of game play...

Edit: Replay Value>Story>Multiplayer>Everything else...

Well said, RolStoppable.

replay value

i dont think that storyline is the most important out of all of those. While it is nice to have a good storyline in a game, and while it will boost how good a game is significantly, it is not the most important imo. If you look at the new mario game for example, the story is the same as every other mario basically, but many are saying it is one of the best games ever.

Hmm, that's a hard question and don't think I can actually answer that one. Gameplay is definitely my number 1 factor 99% of the time, but the other stuff really just depends on the game genre.

storylines are mostly important for rpgs

My friend was drawn through Folklore by the story even when he had got tired of the gameplay