My answer will always be not important; however, I think the art direction that its chosen for the game is key for me caring or not caring for the graphics. Story, gameplay, and music is number one for me, but I also want the game to look aesthetically pleasing. Granted, it doesn't have to be 100% eye candy, but enough to mingle with the other three for a cohesive experience. Like with any other type of media, really - you want the experience to be worthwhile. And it kind of goes without saying, but I also think the generation the game is from has to be taken into account. Although, I'm pretty sure we all can agree that graphics don't equate to quality.
At this point I feel like I'm rambling, so hopefully the words I chose to articulate my thoughts make sense...