Very difficult to decide, as there are quite a few!
I probably spent the most time with
Quake II though, and that's probably my favourite of all. It spawned a lot of popular mods that later made it into Q3A (including my favourite game mode, instagib), also my favourite gun in any FPS ever (the railgun

). There was also a multiplayer mod for it called KOTS (King of the Server) that was basically Quake II with persistent stats stored on a database, with rankings, weapon upgrading and some cool extra abilities etc... probably the most addictive multiplayer mod I've
ever played in any FPS, and it's a real shame it didn't seem to make it into later FPSs (there was a project to bring it to UT 2003, but it never properly took off).
Other favourites of mine include the Doom series (it got me into modding, and is pretty much why I joined the games industry), Quake (again, spent a lot of time modding it) and Q3A, Counterstrike (original, basically up to 1.6), Command and Conquer series (up until Red Alert 2) and honourable mentions for Magic Carpet, Populous III and Dungeon Keeper (amazing to think Bullfrog made three of my favourite games, despite each one being
completely different). I really enjoyed the Unreal Tournament games too (played them a lot), but I wouldn't consider them favourites as I always preferred Quake, the aiming and movement just felt better to me.
Sadly very few recent games make the list

My favourite recent games are probably Team Fortress 2 and Demon's Souls/Dark Souls.