I wouldn't say games have to look 'realistic', realistic graphics don't equal good graphics. I personally thought Mirror's Edge was quite beautiful, although it was not realistic looking at all and not particularly graphically intensive, it was very vibrant and perfect-looking in a surreal way which was really nice to look at. I also think games like Beat Hazard and Audiosurf look great, just those constant explosions of different colors are fantastic to view, but Beat Hazard is basically a sprite game and Audiosurf has very simplistic graphics.
So I don't think games looking good means they have to be intensive on my hardware.
But yes they are fairly important because they help to add immersion. It's not a necessity that my game has to look good, but it does actually add to my enjoyment of a game. Much like great sounds and music will.