This will be interesting.
I'm a PC guy, so all of these are PC games, by the way.
Which is probably why I found Mirror's Edge fun and not shitty.
Let's see here, in no particular order:
Medal of Honor: Allied Assault
The first FPS game and one of the first games at all I played back when I was young. Literally set me up with the groundwork for: basic keyboard and mouse usage, hand-eye coordination and FPS marksmanship skills.
Counter-Strike: Source
My first foray into the world of multiplayer online gaming. Oh, how much my marksmanship skills sucked, how little I hated everyone by default and how much inexplicable fun I had.
Mirror's Edge
The game that taught me both everything I know about effectively moving in FPS games (turning me into a freerunning ninja if a game will allow) and gave me a reason to really try in the first place. I find use of these skills no matter what game I'm playing, from Minecraft to Battlefield 3 to Borderlands.
Ragnarok Online
This game is special to me as well. It was the first co-operative game[footnote]the very first game being Halo 2 on an X-Box, and that was...an experience I'd rather not remember[/footnote] that my first[footnote]and to this day, best and only[/footnote] friend and I played together, as well as being both my first MMORPG and second foray into multiplayer online gaming.
Call of Duty 4: Modern Warfare
This game took my preexisting Mirror's Edge movement skill, FPS marksmanship skill, hand-eye coordination, reaction time, general gaming skill and passive-aggressive animosity towards human beings and turned it Up to Eleven [http://tvtropes.org/pmwiki/pmwiki.php/Main/UpToEleven].
Everything else just kind of expanded from there as I got older.
So, there you have it, ladies and gentlemen.