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: