Lucasart's X-Wing or TIE Fighter remade for the PC. Those were great games. Throw in Grim Fandango and Full Throttle just for good measure. ;)

I've often thought a 2D remake of Shadow of the Colossus would be good. At least it would be interesting translating the exploration part of the game play.

Road Rash 3D. I coldnt tell you how much i played that game. I think that bashing people off bikes going 120 MPH with a crowbar would make an excelent game if you use the endorphin phisics engine (GTA4).

Basewars...

 The only video baseball game I have ever enjoyed.  However, there need to be different fighting modes depending which positions are battling. 

For example, if a batter decides to "charge the mound", then the game should shift to an mode like the  old "Discs of Tron" arcade where the pitcher would attack and the batter would evade and deflect.  They would be fighting from floating discs because the mound and the batters box would blast into the sky.

Fighting between basemen and base runners would be similar to the original (except upgraded with modern 3D fighting mechanics).  You should still be able to upgrade the weapons and armor systems of your bots though (think Soul Caliber).

There would still be models of robot (and the model would affect abilities), but in addition to the tank, flybot and humanoid, you should be able to add transformation circuity that would enable transformations (perhaps into robotic animal forms for extra speed.)  Transformation ability would be very costly, but usable in battle!

Robots would still be perminately destroyed if their health points reach zero, so switching out players and strategy will be a must.

The game should ship with an editor so that you can create your own bots.  The editor should be able to take a common jpeg picture file and "robotize" them allowing you to put yourself or any other character you may want on the team.

 Oh well, everyone can dream...

T'ai Fu wrath of the tiger. I think this was my fav game on PS, so i would love to it redone for the PS3.

The game i personally would like to see remade is Star Wars: Shadows of the Empire. It has quite a cult following, and with the power of today's consoles as well as a new trend of companies updating their movie franchises to video games (like the new Ghostbusters and Star Wars: The Force Unleashed to name a few) I think it would be quite possible this could happen. If you read the novel, Shadows of the Empire is a great addition to the Star Wars universe and really needs to be retold... the N64/PC game didn't really do the story justice, although the Battle of Hoth level was very impressive for its time.

Edit:  @Jedson328... i too would love to see either an update or a full fledged sequel to the X-Wing/TIE Fighter series since i never really got to play them when they were originally released.  Or even a new Rogue Squadron game would make me happy as well.

Goldeneye in High Def.

I never played it, but in HD it would be great.

I want to see Pong remade. Throw in some killer paddles, some dinosaurs, a few ninjas and some hardcore RPG level system and I think we'll have a guaranteed 10m + seller.

 You've never played it so why do you assume it would be great in HD?

I feel you've missed the entire point of GoldenEye, it was amazingly fun because of its four player splitscreen and its simple design. What it really needs is not a graphical upgrade (although it would need that too) but a mechanics upgrade as its extremely clunky by todays standards. 

 Shame on you. You forget that every game will be good if it's remade in hd.