Deus Ex. The story and game mechanics don't need to be changed... they're perfect as they are... but a graphical update, a modern physics engine, more complex AI, and maybe doing a bit with level design (nothing too extreme)... it never gets old, but I'd buy a remake along those lines in a heartbeat.
But there's another I have to throw out there, and I don't think words can describe how much I'd want this: Mechwarrior 2. Throw in the expansion and Mercenaries and I'd be like a little kid on Christmas at the existence of such a remake. To be honest, I'd pay good money just to get the soundtracks as performed with actual instruments instead of MIDI or whatever it had. But those games, with modern technology? If done right, I'd be in gamer heaven.
I'd also like to see a remake of Fallout Tactics that adheres much more closely (in both story and more minor details) to Fallout canon and aesthetics. Better graphics, too, though if you got rid of the sprites you'd have to have some way to keep those creative and violent death animations more or less intact, it just wouldn't be the same otherwise. Now, I don't like Tactics nearly as much as Fallout or Fallout 2, but I still had a lot of fun with it and I think it's a fine game in it's own right.