Is it possible to get free multiplayer games on steam?

Unless the game specifically notes itself as "Free to Play", you'll have to buy it in order to play it. I DO NOT RECOMMEND ATTEMPT TO USE ANY CRACKS OR HACKS WITH STEAM, as they generally will not work & likely get your Steam account banned in the process.

WIth that said... there are legal options to get the games for free OR near-free. Bundle sites like Humble Bundle will sell games (a good amount with multiplayer) for fractions of retail (up to 98% off) in bundles. While base bundles require a minimum of $1 for Steam Keys, paying more will get you more games.

There's also giveaway sites like SteamGifts.com that run on a raffle system. Users periodically earn points (at a rate of 5% of the points value of each new drawing added to the site) that the redeem to a raffle of a particular game (1 point per dollar the game retails for). Odds of winning are based on number of entries, so odds will vary between 1.000% to 0.001% (depending on the popularity of the game being raffled off) most of the time. Odds can increase up to 50.000% in mass raffles (where there's around 1,000 or so copies available in a raffle), but these are fairly rare events that are sponsored by the developers of the game.

Pestering friends & family members to gift you the game (or Steam Wallet prepaid cards) is viable as well, but may not work as desired (since people don't like get constantly badgered, especially when there's no justification for it).

Yes, it is possible to get free games on Steam. Ask someone you know to purchase the game or to give you the equivalent money (whether actual money or prepaid money for use on Steam) as a gift for your birthday, Christmas, or some other gift giving reason. This way you get the game for free since you aren't out any of your own money, and you don't have to worry about problems arising as if you had tried stealing it.

If a game requires Steam, there is no way you can get it without buying it or receiving it as a gift.