Frankly, since I've been gaming since 1979, I could make a list that would take aeons to read. But I'll keep it to a few favorites.
Final Fantasy I, IV, VI, VII, VIII and Tactics
Zelda, Zelda II, Zelda LttP, Zelda Link's Awakening
BLASTER MASTER (Greatest NES game EVER!)
Pac-Man
Galaga
Gauntlet
Mortal Kombat (GET OVER HERE!)
World of Warcraft (Even though I don't play anymore, I did enjoy it at the time.)
Diablo II
Ninja Gaiden (Old Nes one, not the new ones.)
Secret of Mana
Fallout: New Vegas
Metroid, Super Metroid, Metroid Prime
Castlevania in all it's silly formats
SaGa Frontier (Obscure game. Most people don't know it, most that do hate it. I love it, I'm weird.)
Wild Arms
Donkey Kong
Super Mario Bros. (Before it got whored out.)
Sol-Feace (Even more obscure.)
Chakan the Forever Man (I'm the only person on the planet who has beaten this legitimately. No cheat codes, no save states.)
Doom
Star Wars: X-Wing and TIE Fighter
Star Wars: KoToR
Mass Effect 1&2
Dragon Age: Origins
Minecraft and Terraria
Team Fortress 2
Day of Defeat: Source(Even though I suck at it.)
Saint's Row 2
Bioshock
And the Civilization Series.
I could go on and on and on, but I don't want to look too much like an obsessive compulsive geek.