The remake of Bad Dudes and River City Ransom is The Warriors. I know it's actually a prequel/remake of the movie, but if you think about it, if they wanted to make an amazing gang-war beat-'em-up, it would have to be an updated version of The Warriors to be any fun. The same for Final Fight and Double Dragon.
I'm really looking forward to the remake of Shadowrun. I'm extremely disappointed that they're classifying it as a First-Person Shooter, but I'm hoping for the best on that one. If I were to make a remake of ANY older game, I must say I would remake
Blade Runner as a Massively Multiplayer Online Role-Playing Game. It would be cool to be able to choose between being a bounty hunter, replicant, police, and citizen. Bounty hunters can get missions to kill replicants. Replicants could look like any of the other classes as a means of hiding, and get missions to wreak havoc and try to free your 'people'; protecting them from the bounty-hunters and the police. Police can get crime-fighting missions and occasionally come across replicants to retire, and therefore clash with the bounty hunters. Citizens could build and run shops, stores, or just choose to either live peacefully or go crazy due to lack of contact with other people. The crazy thing is everyone would have to keep each other from thinking they're replicants, no matter if they are or aren't.