Uhhh there are too many games that should be remade, but ill just list a few. (Kid Icarus is obviously one other people have shown interest in, so Ill keep off that topic)
Double Dragon- I would like to see a new Double Dragon come out for the Wii, or when Microsoft releases Project Natal, use like the new Punch Out style controls (with WiiMote and Nunchuck). I personally think it would be a pretty big hit since it was back in the arcades and classic consoles.
Duck Hunt- Lol, I think so many people would enjoy this game with the Wii, using the Wii Zapper or making a new Zapper/Light gun design. I think it would do well because if you had or have a NES, chances are you have Duck Hunt and from what Ive seen its one of the most recognized games on the NES alongside Super Mario Bros.
Mario Paint- Could be almost like a Wii Sports sort of thing, maybe and using the WiiMote to point and paint etc. Also I think allot of people would enjoy a new Mario Paint Composer on the Wii
Those are some of the ones that would make sense, another one Id like to see is Star Fox, but Im not quite sure how it would be. Also remaking an Atari 2600 game wouldn't be a smart idea at all. Most people probably wouldn't catch on, or they are so basic they would flop
Also, the worst game ever made, E.T. should get remade. I think with the right script and idea it could be a good game-made-from-movie. Not like the piece of junk for NES where you pick flowers and dodge holes.
Its not for the NES as already mentioned and you don't pick flowers or dodge holes. You go in the holes to find pieces of a phone, in witch you collect to "phone home" while being chased by the government. Not trying to be rude by saying this but don't bash a game when you don't know what its about (not saying its a good game in any way I agree it was bad)