For me there will always be one game that is more deserving of such a remake than any other...
Star Wars Ep 1: Racer.
https://www.youtube.com/watch?v=t8FVL46rZm0
Dated as it is, it holds up beautifully, and it still remains to be my favorite racing game of all time. Even with the limited hardware of the time, they did an amazing job in their texture work to make it at least ~feel~ like you were racing at hundreds of miles an hour, in all the environments that were so varied and beautiful. As you made your way through the tournaments, sometimes you'd revisit old worlds but explore new parts of the track, and see even MORE crazy-cool environments. I don't think it'd warrant even the cheaper $40 tag that most remakes get, but I could see it as a $15-$20 release on Steam, PSN, and XBLA. Although personally I wouldn't hesitate to drop $60 on it because I love it so much, but that's probably just me, XP
I know it's sort of a niche choice, but still it's one of my favorites. I'd like to see other old Star Wars games remade as well, like the Dark Forces and Jedi Academy games.
While I'm at it, there's also some other older titles: Freelancer, Black & White 1 and its expansion Creature Isle, the MegaMan Legends games, any or all of the MegaMan X series, aaand I think Final Fantasy 7, 8, and 12. Can't really think of anything else that hasn't already been made. Yep.