It varies by genre, also, that list fails because there's no story catagory so I refuse to show my rankings.

Gameplay
Replay Value
Music
Innovation
Graphics

1) Gameplay

2) Social aspect

3) Innovation

4) Graphics

5) Sound

I think people keep thinking "wii" when they read innovation. Aiming down a sight, that's an innovation. AI that flanks or reacts to you're approach is innovation. RPG System in CoD4, innovation. I can't remember which game did it but mapping weapon change to d-pad, innovation. Separate ball and player physics, innovation.

If we didn't have innovation, you'd all be complaining we are playing the same old game each and every time (like what FF's and turn based JRPG's went through) and we'd all be playing Pong still. This is a increasingly big issue in the FPS console market, seeing as how every game now needs a pull or else it's deemed as just another clone.

You may not rate it highly, but you'll raise hell if you don't get it.

You sir are priceless!

OT :

1. Gameplay ( By far the most important part for me)

2. Social aspect ( Except for RPGs, I don't want anyone bothering me when I play them!)

3. Sound

4. Graphics

5. Innovation ( I'm buying Megaman 9 on release, so it shows how much I care about innovation)

Quick note : I don't think innovation is a bad thing but a game doesn't have to be innovative for me to consider it a great game.

Gameplay
Graphics
social aspects
Innovation
Sound

You can always lower the volume if you don't like how it sounds and most games come with subtitles lol.

Uh, weird criteria. Well, given only those 5:

1. Gameplay.
2. Innovation.
3. Social Aspect.
4. Sound.
5. Graphics.

If you must know why I think sound could be better than graphics, it's because I get bad music stuck in my head driving me crazy for hours after I put the controller down. But I don't get bad graphics stuck in my head driving me crazy later.

@CAL: Not really, I don't expect every single game to be innovative, and if dev's strived towards that as a main objective, the other points would suffer effectively making games boring and ugly (a little roughly formulated).
I've played quite a few games that were innovative, sadly though, most of them just weren't fun or looked mediocre or has bad sfx or a poor score, fiddly interfcae and what have you.
No, I'll stand by my list, so long as the games take small steps in positive directions now and then when it comes to innovation I'll take gorgeous, well playing, good sounding games any day over fud with no goal save for being "fresh".
Of course, there are games that have all points in abundance, but those games only come around every three blue moons I'm afraid.

Don't you like Ass?

Nice list... I wonder where you rate Exploding Crates/Boxes/Barrels?

1. Gameplay
4. Innovation
2. Sound
3. Social Aspect
5. Graphics

For the given 5 it would be...

1) Gameplay
2) Sound
3) Innovation
4) Graphics
5) Social Aspect

For me it's...

1) Gameplay
2) Sound
3) Presentation
4) Storyline
5) Graphics