For the PC, Half-Life 1 and 2 and Portal, great puzzler-comedy. Doom Deus Ex Elder Scrolls: Morrowind and Skyrim (although skyrim is a bit watered down, but thanks to the modding community) CoD4 and Crysis 1. I guess.
Oh, and GTA 3, It revolutionized open sandbox gaming,
Battle Zone Tetris Mortal Kombat Space Invaders Pong (lolz) Super Mario World Ace Combat Morrowind Fable Lost Chapters Wing Commander Kirby's Dreamland Star Craft
Here are my favorite PS2 Games. (RIP Satin Silver PS2)
Area 51 Burnout Series Call of Duty 2: Big Red One Crash Bandicoot: The Wrath of Cortex & Twinsanity Grand Theft Auto San Andreas Jak and Daxter Series Need For Speed Underground, Most Wanted, Carbon, Undercover Ratchet and Clank Series Simpsons Hit & Run Star Wars Battlefront 2
Here's a list of the games I feel are the greatest Wolfenstein 3D Doom Samurai Shodown Quake Metal Gear Solid Mortal Kombat II The Legend of Zelda: A Link to the Past Tenchu - Stealth Asssassins
Art of Fighting The Sentinel Armalyte Castle Quest Head Over Heels San Andreas GTA IV Vice City Jetpac Half Life 2 Crysis Star Wars Thanatos F.E.A.R. Turrican II FFVII Another World Tekken 3 Starglider 2 Ghosts N Goblins Mario Kart Street Fighter II Operation Wolf Time Crisis Portal Gran Turismo 2 Far Cry Flashback Abe's Exodus Buggy Challenge
All of these games have made me say to myself "OMG! THIS IS GREAT!!"
TES III: Morrowind - Can't count how many hours I spent on that game, it's truly amazing experience. In my opinion, still the best game in the series, because of its unique atmosphere, music, and story in general!
Civilization series - I love me some good strategy game, and Civ series offer even more than I ask for. Lots of replayability, nice modding community, and that "one more turn" syndrome.
The Witcher series - Even though I'm pretty new to The Witcher games (and books), I loved every minute of it. Really mature and well executed RPG! Great story, lively characters, amazing graphics and music. I'm really looking forward to the new one to be released!
Dark Souls: Prepare To Die Edition - My honorable mention. Started the game without any prior knowledge and expectations, and got completely sucked in, then punched, smashed, sliced & stomped. Really refreshing experience in a time where every other game holds your hand and guides you every step of the way.