Here's my list:
-Demon's Souls/Dark Souls: THE Best game of 2011 (with Skyrim), it has a good story, an interesting world, the music is awesome also, it's how games were back then. They throw you into this world and let you discover everything by yourself. It's THE game that draws the line between Casual gamers and Real gamers.
-Silent Hill/Resident Evil: The two series leading the Survival-Horror genre. Probably one of the best game genre in history because it was the beginning of games with deeper stories than usual. People should at least try one of the games from the two leading series. Im talking about Resident Evil 1,2,3 and (to some extent) 4.
-Killer 7: A game visually striking with an incredibly complex story.
-Kirby Superstar: My favorite game ever and a milestone in platforming and in video game music.
-Unreal Tournament 2004: During a certain period, arena shooters were really popular (Quake 3, Tribes, Return to Castle Wolfenstein, Unreal Tournement) but UT2004 is THE absolute best arena shooter...EVER. The music was fitting, the guns were awesome and the single player was really fun and challenging.
-Lunar 1 and 2: A JRPG with a really good story with a lot of twists and turns, good characters, good music and fun combat.
-Twisted Metal 2 and Black: The two best car combat games in history with an incredibly dark story, good music and cool characters.
-Earthbound: Incredible Story, very cool music, fun combat and funny dialogue and enemies.
-Mega Man 3: A milestone in platforming with incredible music.
-Super Mario bros 1, 3, Super Mario World and Super Mario World 2: Yoshi Island: Milestones in platforming and also games that are really really fun to play (especially Super Mario World 1 and 2).
-D0OM/Goldeneye 64: The game that put FPS on the map and still in the top 3 (Doom) and the first game that tried something different with the genre.
-Myst: One of the most complicated adventure game in history, this game will make you ether swearing your heart out or make you beg for more.
-Kingdom Heart: A twist in the JRPG genre with probably the most unique story to date.
-Counter-Strike: Source/Team Fortress 2 : Still two of the most fun games to play on your PC online.
-Duke Nukem 3D: Still one of the best FPS in gaming history. A game that is a required try when you look at today's industry.
-Gran Theft Auto: Vice City: THE best GTA ever, great music, great characters, a story that is a mix between Scarface and Carlito's Way, very varied missions and a spot-on 80's feel.
-Elder Scroll SKYRIM: A really really fun RPG with a great environment and a lot to do.
-Manhunt: Still one of the most violent games but also one featuring some of the funniest NPC's in video game history. Also, with an original story and great controls.