Um... World of Warcraft? Ha, just kidding. Half-Life... OK, seriously now.
I remember some epic games that are nearly unknown these times. Which is a shame. Like Jagged Alliance 2 - veterans might remember. I still love this game, it's a classic and it's still awesome to play.
From newer games, I pick Vampire: The Masquerade - Bloodlines. This RPG is probably better than any Elder Scrolls game - it just has some flaws and mistakes, but it has left an impression on me that I will not forget.
And I'm sure you've never heard of Obulis. It's a relatively small independent puzzle game with nice graphics and very well-done puzzles based on physics. I got it on Steam, not knowing what to expect. I was positively surprised.
And, uh, Mario...? OK I'LL STOP NOW