I find it funny how people compare women with games

For me, the better the graphics. the better the game. But they alone can't make up for bad gameplay, story, soundtrack etc.

Gameplay is still the most important factor for me.

The overall presentation matters. Sometimes the higher graphical power makes things look far better than it otherwise would - my favorite looking HD game this gen would be Gears of War. The game's art/graphics make it pretty damn immersive, the same effect would be slightly diluted on the Wii.

However, "Graphics" nowadays seem to refer to all the technical effects thrown in a game, something I definitely don't care much about. Games that strive for realism I find to be pretty boring. That actually plays a major factor in why I prefer Japanese games to most western ones. My favorite western devs (e.g. Blizzard) go for a more cartoony look, if not 2D (SC/Diablo). Hell, I loved 2D sprites, it really sucks how 3D has almost replaced it entirely. I want a modern day JRPG done with sprites, FF6 / Chrono Trigger style!

I think graphics are very important, not in general but to the particular game. Think about the Wind Waker. That entire game's atmosphere was created by it's striking cel shaded graphics and they added immensely to the experience.

Graphics themselves don't make the game, but some genres they sure do help. Put simply, Uncharted 2 would not be so immersive nor engaging with its characters if the graphics were weaker.

Basically, I find the more there are characters, dialogue and a story, the more graphics matter - so long as they don't affect gameplay obviously.

Drake works better as a character for me because he has fine detail of expression, and realistic animation, and his adventures take place in a detailed world.

I look at graphics like special effects in a film. They can't save a bad film, but they can improve a good one.

Whatever works best.

Uncharted 2 relies alot on immersive, well lit heavily detailed environments to set the mood.

Gran Turismo has always impressed me on how realistic it looks, but then when I see a jaggy shadow cast down the side of the car it takes away from the experience.

Good graphics is why I bought a big HD tv.

Oh. I get you now. You do think graphics are important, but anything better than RE4 or TP is just gravy.

Precisely.

Graphics add to a games feel, and hence, can make the game better.

Uh I think a game should look good within it's own terms.
Like, for me (in my opinion, you see) a pretty SNES game looks better than any N64/PS1 game simply because both consoles can't bring themselves to render some decent looks. I don't know, it's just that the 5th generation is the uncanny valley for me, and that totally ruins the gaming experience (I would not give a single N64/PS1 game a rating higher than 7).
In the other hand, both Zelda:WW and SMG are examples of games with amazing visuals, because they accomplish their intents, so to speak. Maybe one could add Wii-series games into this list...
For last but not less important, some kind of games - like shooters, action and RPG games - should always look for the best visuals unless they seek something else than photorealism (like the already mentioned Wind Waker).

Majin is the type of guy who goes for drunk fat chicks