Story, character design, effects, FMV/CGI movies and graphics in no particular order.

I can play old games with bad graphics because I understand the "power limitation" of their time but I will not play a PS3 game that looks like FFVII!

 You have a 360? Do they have nintendo characters now?

Well the most important as you say is gameplay. Which is different in many games.

Theres the standard way of thinking of gameplay. Dual stick shooting, ir aiming, x (throw grenade), ect.

Then theres the other smaller but I think more important for at least games I like to play more. (not a huge FPS fan) Like for me FF3 I was not a fan of the class systems. This made the game a huge turn off for me and never actually finished it. Reached a lul point in story and becuase of the leveling system I got annoyed and quit.

But if the gameplay is good enough to be able to tollerate playing the game, then the next is the story. If the story or game setting is something you don't like then you will quit playing as well.

Character design and graphics mean nothing, they are just simple things on the box and commercials to sell the game. When thinking back on games the last thing i remember is how the characters look and what teh graphics were (which usually my memory makes them better than they were) When i think of a game i think first was it fun. Which makes me think of the story and also I think of annoyances such as bugs or control problems.

Creativity, how different it is from other games...(and gameplay)

atmosphere as well. i like to feel as if i am in the game. and i have to like where im going.

when I BUY a game, it's important if I will play it again once I finish it (if it's that kind of game). games such as Mario Kart, Civilization, etc, do not suffer from this, unless the multiplayer is not that good or I won't find a lot of people willing to play the multiplayer.

I dunno if it fits in gameplay, but one thing that really puts me down is frustrating difficulty, when you play a long part, die, then have to replay it again. kinda like the Magnificent Five chapter in Viewtiful Joe, that I haven't cleared since I got the game two years ago.