Not sure if any of these are the best online games ever, but certainly my personal favourites over the years I've been online gaming...
Star Wars Galaxies - Played it for 2 years and was my first proper rpg, which I wasn't a great fan of, but was getting bored of FPS'ers and wanted something with more depth. (Amazing how many people are still so passionate about this game and want it back, pub 6 reewind!)
HL: DM - Amount of money this cost me, back in the day, dial up and my marriage, most probably..
BF1942 - DC mod - Had some wicked laughs online with this great game/mod.