With the Resident Evil 2 remake being fucking amazing and a remake of Link'a Awakening on the horizon, game remakes seem to be an in-thing right now. I'm not just talking graphical upgrades either, like say the great Super Mario All-Stars. I'm talking a remake that upgrades graphics and improves upon gameplay and maybe even story from where it began. Maybe add entiely new levels to the game.
Here are what I consider to be prime candidates for remakes:
Castlevania 2: Simon's Quest- Upgrade to 16 bit graphics, fix the translation and improve the day and night cycle.
Sonic Adventure 1 & 2 - Graphic upgrade, game play upgrade. Maybe cut Big The Cat and add different character like the Chaotix Crew(or just Mighty the Armadillo).Debug the shit out of it. Maybe have a mode where Tails can leave the Mech. Improve the Knuckles levels a bit.
Sonic 06 - FIX EVERYTHING. Every fucking thing. No more bugs. Make it a great 3D platformer instead of the buggy mess it is.
Knights of the Old Republic - Keep the core but improve everything like Wonder Boy: The Dragon's Trap did.
Shadows of the Empire - Keep the plot as intact as possible but almost total gameplay overhaul. Again, look to how RE2 did it.
Dark Forces/Jedi Knight series: Look to how Bethseda redid Doom. There's the blueprint