To me, the idea behind remakes is to make games that we all loved from yesteryear actually playable to a modern audience.
Let's take an example - say, the original Metroid. Give it to a modern gamer. Chances are, they'll give up after about 10 minutes, because the levels are absolutely huge, you've got no idea where you're going and and progress, if any, is slow. Give a modern gamer the remake, Zero Mission, and they should be quite content with it. Still big, but it's a lot more accessible, you know roughly where you're headed and, provided you're not concerned with those hidden power-ups, it runs at a pretty good pace. The gamer is happy, and the remake is a success!
With that in mind, an awful lot of NES and Master System games could do with a remake - the original Zeldas, for example, could benefit from a 3D engine (and a plot [No! Bad Darthy!]), or at least a more streamlined gameplay mechanic. Ask a modern gamer to play the first Zelda and they'll have no idea where to go, which is hardly conducive to good gameplay. Also, updating Metroid II so that it's as playable as the other 2D Metroids (and in glorious colour!) would be a smart move on Nintendo's part.
Some other suggestions I've seen here that I can happily ridicule...
System Shock 2: This is perfectly playable on modern machines, especially once it's been updated with better graphics [http://www.strangebedfellows.de/index.php/board,2.0.html]. It's just hard to track down. The sooner it gets put onto Steam, the happier and poorer we'll all be.
Splinter Cell: Again, don't need remaking at all. Just fixing. And they're not even classic gen - all of them came out on the PS2!
Conker Live and Reloaded: This itself was a remake of Conker's Bad Fur Day, a game that desperately needs a sequel lest Rare be lynched.
Zelda Link to the Past: They already remade this. They called it Twilight Princess. Zing!
...kidding. But the similarities are remarkable - Light and Dark World, Link transforming into bizarre creature upon entering, original villain actually being controlled by Ganon, etc... Why would you want to remake a game into something that, even allowing for the similarity of Zelda games, would be remarkably similar to another one?
Final Fantasy VII: My views on this game are irrelevant, and I will not discuss them her-IT'S ABOVE AVERAGE AT BEST AND PEOPLE ONLY LOVE IT BECAUSE IT WAS THEIR FIRST 3D RPG!
Oh that felt good to get out. But remaking it would be pointless, because they'd bring absolutely nothing new to it. It's already in '3D', all they'd do is make it look prettier (which dedicated fans have done for the PC version already). It's full of side-quests, adding more would only put people off. It's got plenty of characters, and changing even one thing about them would infuriate most of the very people the game is being made for. Why bother?
Metal Gear Solid: They already remade this for the Gamecube. [http://en.wikipedia.org/wiki/Metal_Gear_Solid:_The_Twin_Snakes]
Aladdin: Yeah, some Prince of Persia style agility would be interesting, but you wouldn't be able to kill anyone (a Disney character, committing murder?), so I doubt if it would really work that well.