I'm on the PC, so depends how old it is, and how much I liked the original. Backwards compatibility has never been a problem here.
Warcraft 3. Love it. If they came out with a HD version with updated graphics? Gimme. Gimme now.Thankfully I think they were supposed to be releasing a patch that would update it to run better on HD setups, even though the graphics likely won't see an improvement.
Stronghold series. They're starting to look pretty dated, but its rare to find games with the same features. I'd buy them and play them.
Hell, to be honest, its half the reason I've bought every Civ since 1. The slightly different gameplay is a cherry on top, though sometimes [Vanilla Civ V] its just the pip. Getting to play Civ, but actually looking decent instead of looking its age? Yes please.
Bioshock though? It'd want to be one hell of an improvement. I'm talking Crysis level graphics or better here. The old game looks slightly dated, but with its art style it works, and it really still doesn't look bad. Same for 2. Same for 3. It'd have to be an incredible upgrade for it to be worth it, which I honestly doubt it will be.
But yeah, if I love the game, and it just doesn't really hold up to modern standards, or if there's a really high end improvement on it, I'll get it. Sure, graphics aren't everything, but sometimes they are noticeably old, or the new ones are truly incredible and that's a selling point to itself. So long as the gameplay is good though. I mean, I'd buy something just for its amazing graphics - if it was cheap. For a full price game? Yeah, gonna need good gameplay and good graphics there.