Well, there obviously isn't one answer, and since I do most of my posting in short burtsts of time, ill post any little insight I can think of
cohesiveness
I'm not sure its even the best word, but everything needs to fit together perfectly. Play street fighter 2 or 3 for example, when you press the button to punch, the speed of the animation, the size of the hitbox, and one people overlook, slight delays between the sound effect and the reaction animation, these are things that make the game feel so solid. A slightly longer or shorter between hit and reaction animation or sound effect creates a completely different feel. I think putting the love into these details separates the ok games from the great games. That was an example on a small scale.
Take littlebigplanet, a masterpiece in my opinion. The art style, the sound effects, the music choice, even the choice of the voice for the narrator, it all speaks the same language.
And btw, my personal take on graphics is that people understate their importance routinely. Because it seems superficial, like saying you like a girl for her looks rather than her personality.
But I think graphics do matter, a lot. A game can't be great with only good graphics, but I would say most great games do have great graphics. Even indie games that don't have impressive graphics, any of the ones I've thought were great always had some type of charm or cool lookingness. Even something like plants vs zombies, world of goo, braid, or torchlight. They look good. Not like gears of war, but good in their own way, and back to cohesiveness, notice they all look and sound uniform, no unfitting fonts, no mismatched color schemes. I think the difference between successful and unsuccessful indie games a lot of times is that last bit of polish that brings it all together