None, I believe in the saying "If it ain't broke, don't fix it." Especially because no matter how good the remake turns out, people will whine that it "isn't as good as the original", and they usually aren't, in part because people have rose-tinted-glasses when they think back on their favorite games, and in part because it's hard to capture the spirit of the original in a remake, especially if the levels don't transfer over well, or you try to add stuff but then get carried away and it isnt a remake or something, (most games change a lot of things up so that it isn't a straight remake, I think) - games like Sonic 2006 and that new Prince of Persia were both remakes and got pretty negative reviews.
You can make all the sequels you want and I can count them as new games with the same characters, but if I'm playing Super Mario Brothers "in 3d!" like these new Super Mario games all try to do, it just doesn't feel the same, though the games are fun and capture the motions of the originals, to me, it feels weird to be playing a sidescrolling Mario game with a gimmick and a 3d model that is trying to imitate a sprite or something.
I dunno. I'm sort of torn in that I think they should try to bring back the spirit of old games, but I dont know how they would do it.