It all depends on the game. I will still play classic games if I still like them, but I do have a cut-off point for graphics.
Though this may not be classic, Madden 07 for the Wii is a prime example. Normally, I freakin love Madden games, but I was extremely disappointed when I played the Chicago Bears. It looked like they were black blobs on the football field, hardly any detail to them at all. The 'Create-A-Coach' was always a problem in Madden games too. They just seemed so... bland, uninspired, blah! I couldn't stand it at all.
For older Pokemon games (Red, Blue, Yellow etc.), I have absolutely no problem playing them. Yeah there are a few glitches in the graphics, but overall it's nice, simple, and fun. It's games like Pokemon Dash that give me a problem. They are failed experiments at 3D graphics and, to be honest, they looked horrendous and slow the game down enormously.
That's why I normally play my Xbox and 360. They have great games and amazing graphics (save for Lara Croft, Madden 06, and the oh-so glitchy NHL 2K6). I... really can't stand my Wii. There haven't been many good quality games and the rest are just party games for the whole family, and as an only child, that's a major turn-off for me :/.
Basically, the graphics can be a bit lacking, but the developers have to make it up in the actual game play. I don't mind going back to play a round of Tony Hawk for the N 64. The same concept goes for great-looking games. I don't know many off the top of my head, but I know they're out there. These games look great, and yet their story/game play reeks of... yeah. It's a big-budget bust :/.
Graphics are an essential part of the game, but they shouldn't make the game play suffer :).