Team Fortress 2 from Valve is one of the more MMO-like first person shooters running. It's only played online, is class-based, has achievement unlocks which open up new gear possibilities, and after the last update there's a backpack with room for 50 items and mention (read: unconfirmed) of tradeable items. In some ways, TF2 is an FPS for MMO lovers -- or just those who use way too many acronyms.
The comparisons between Team Fortress 2 and MMOs aren't lost on some of the more inventive TF2 players out there like goldenhearted who's made Garry's Mod mockups of a fictional "Team Fortress 2 RPG". Valve also got in on the fun in a slightly sneaky way in the latest game update. Steam users found this programmer's tip of the hat to MMOs in the game code:
// TF2 MMO
"TF_MMO_LFG" "Looking For Group"
"TF_MMO_Quest1" "You must kill %s1 %s2 to complete this quest."
Nice one, Valve. And congrats on successfully departing from the standard FPS formula and hooking at least half of the Massively staff on TF2 in the process. We're not sure whether we love you or hate you for that, honestly, but if you're reading this... Spy class update soon?