EvE Online - you don't get much more multi-player than that
Not cheap, though you get what you pay for with EvE - a vast, busy and varied universe with continual development and upgrades.
Original Everquest is now F2P and now it has been (unfortunately) repeatedly bludgeoned with the simple-hammer is entertaining for a few weeks and is busy if you stick to the well-trodden paths.
Also have to +1 TF2 - exceptionally well rounded game that you don't have to pay for ever if you don't want to. The light-hearted style doesn't detract from the game play quality and is so refreshing after countless 'end of the world and only you can save them' scenarios in other games that takes themselves far too seriously!