depending on your specs you could try planetside 2 beta which is open now i think... i downloaded an had a game a few weeks back after i got my invite and its pretty good... in fact very good for a free to play...
theres also some free to play games like battlefield, battle field heros. you just sign up and download then start playing. both have reasonably good sized comunitys so you wont struggle to find a game...
on steam theres also team fortress 2 multiplayer which is free. again v good.
if you are in to MMO's you can check out SWOTR and LOTR online, i found Old republic better than LOTR. also my favourite for lan parties are Battlefield series mainly 1942, also Unreal tournament, Savage 1 or 2.
If you have Steam, then you probably received several copies of Dota 2 for free. I'm not a terribly big fan of the genre since it's just watered down WC3, but it's highly populated, somewhat harder than League of Legends, and less pay2win scammy.
Team Fortress 2 is another game that is still highly populated, extremely fun to play with people, and has a huge skillcap so you don't have to worry about peaking early. I'd recommend this game the most actually, since it's free to play and the default guns that you get for free are in most cases more well-rounded than the premium guns (which you can also discover as you play, albeit slowly).
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!