Aged well: Super Mario Brothers. Graphics that aren't eyesores, fun to play, a classic and probably always will be.
Star Fox 64/Lylat Wars. This game holds its own to this very day with some still very top-quality gameplay, replayability, crisp visuals and memorable music.
Quake III Arena. Still an absolute blast to play, low system requirements means it's very accessible, and with Quake Live coming soon, the Quake III experience will be around for a long time.
Need for Speed 3: Hot Pursuit. May seem like a weird choice, but this game is still awesome arcade driving fun in its purest of forms. Why can't they make NFS games like this anymore?
Death Rally. Another game that needs more attention. For the uneducated, it's a top-down racer with weapons, where you have to work your way up through the ranks of the competition (not to mention Duke Nukem) to defeat the Adversary. It's such a blast to play, just a bit of a pity it's marred by compatibility issues with XP.
Aged badly: Star Fox/Starwing. Revolutionary for its time, sure, but with SF64 around it just doesn't stick out anymore. (nice music though)
Duke Nukem 3D. It's still fun to play, but after a while you kinda tire of the dated feel of it all. Which makes Duke Nukem Forever all the more necessary.
Donkey Kong. Meh, it just seems somewhat unsubstantial now.