Here is a list of my favorite games sorted by genre:
Action - Platformers
Super C (NES) - Still my favorite from the Contra series.
Mega Man II (NES) - My favorite in the series because you can beat the bosses with just the Mega Buster.
Super Mario Bros. 3 (NES) - I never get tired of this game.
Super Mario World (SNES) - Likewise.
Adventure - Puzzle
Space Quest II: Vohaul's Revenge (DOS) - Hilarious adventure, though annoying walking death areas.
King's Quest V: Absence Makes the Heart Go Yonder (DOS) - Not the best story, but the best graphics and speech.
Adventure - Platformers
Bionic Commando (NES) - Sharp learning curve, but wonderful story and game play.
Castlevania: Aria of Sorrow (GBA) - More of the same, but tons of fun.
Castlevania: Circle of the Moon (GBA) - I love the card system.
Metroid II: Return of Samus (GB) - Much better than the first as far as play control and story.
Metroid: Fusion (GBA) - High pressure situations with being stalked by an evil Samus.
Metroid: Zero Mission (GBA) - Wonderful remake and expansion.
Fighting - Arcade
Garou: Mark of the Wolves (ARC) - Gorgeous graphics, good mix of fighters, annoying AI.
Street Fighter II: Championship Edition (SNES) - Evil AI, but great for 1-on-1 friend play.
Shooter - First Person
Doom II: Hell On Earth (DOS) - Entering God mode and killing demons is my Zen moment.
Half-Life (DOS) - Extremely terrifying at times. Wonderful, though the story gets crazy at the end.
Magic Carpet 2: The Netherworlds (W32) - Very unique idea, extremely fun and challenging. Lame ending.
Ultimate Doom (DOS) - Always a joy to return to this FPS.
Shooter - Scrolling
Raptor: Call of the Shadows (DOS) - I love games that let you permanently upgrade your ship.
Strategy - Building
Sim City (SNES) - My favorite incarnation of the game.
Strategy - Combat
Age of Empires (W32) - A wonderful RTS with enough customization to prevent it from getting old.
Wing Commander: Prophecy (W32) - Pretty lame acting, but memorable characters and a kick ass engine.
Puzzle - Action
A Boy and His Blob (NES) - Too short, but very imaginative.
Portal (W32) - Too short. Love the portal mechanic. GlaDOS and turrets creep me out.
Puzzle - Adventure
7th Guest (DOS) - Awful acting, but creepy story line. Some puzzles were unfair.
Loom (DOS) - Wonderfully beautiful graphics and music. Very creative story.
Shadowgate (NES) - My favorite of this style. Only one annoying puzzle, lots of thinking outside the box.
RPG - Action
Chrono Trigger (SNES) - Beautiful graphics, unforgettable music, very cool and unique combat system.
Diablo (W32) - Wonderful dungeon crawler with all the trimmings. Amazingly detailed enemies.
Final Fantasy III (SNES) - Cheesy story, but memorable characters, amazing music, awesome combat.
The Legend of Zelda (NES) - The start of something amazing.
The Legend of Zelda: A Link to the Past (SNES) - A sequel worthy of the original.
Secret of Mana (SNES) - Wonderful music, beautiful graphics, excellent combat, inventive story.
Ultima VII: The Black Gate (DOS) - I love the adult story and sinister elements. My favorite Ultima.
Mike Tyson's Punch-Out!! (NES) - A lot of fun because they don't get hung up on the rules of boxing.