For me it really depends on the game. For example, I love classic games, I play them all the time, so when I play mega man or the nes castlevanias, that's not an issue to me. But when I play something like LA Noire, graphics are important because they help to make the game seem more real and help me to dive in deep into the game. You couldnt pull off that game the same way 15 or 20 years ago, even 10 years ago. I think the more serious and deep the game is, graphics become more important.
Though I feel that games can be fun no matter how they look, I do think they're important to certain games.