How old does a game have to be to qualify as a 'classic' games? I've seen KotR (current or last-gen console, even more recent on PC). I personally would say a game should be at LEAST ten years old (so no Starcraft, Metal Gear Solid, Heroes of Might and Magic 3 or Alpha Centauri, for example).
Anyway, the following is by no means an *exhaustive* list, since I would replay virtually any game I considered worth playing originally. These are just ones that leap to mind:
Bubble Bobble
Cauldron 2
Champions of Krynn
Crossroads
Curse of the Azure Bonds
Dark Queen of Krynn
Day of the Tentacle
Death Knights of Krynn
Doom
Doom 2
Eye of the Beholder
Eye of the Beholder 2
Final Fantasy 6
Final Fantasy Tactics
Gateway to the Savage Frontier
Heroes of Might and Magic 2*
Loom
Lufia 2
Mario 64
Monkey Island 2 LeChuck's Revenge
Phantasy Star 2
Phantasy Star 4
Pools of Darkness
Secret of Monkey Island
Secret of the Silver Blades
Shining Force
Shining Force 2
Sonic the Hedgehog 1
Sonic the Hedgehog 2
Sonic the Hedgehog 3
Sonic and Knuckles
Tactics Ogre
Treasures of the Savage Frontier
Ultima Underworld
Ultima Underworld 2
Wild ARMs*
Wing Commander
Wing Commander 2
X-Com: UFO Defense
X-Wing vs. Tie Fighter
* These two are the biggest question marks, Heroes 2 because Heroes 3 (which is narrowly edged out of my 10-year timeframe) is almost strictly better, Wild ARMs because there was a PS2 remake that's almost strictly better. Heroes 2 belongs, if nothing else, because of its campaigns.