Although limited, there is an increasing number of F2P (Free to Play) games available on Steam for Linux. Below is an overview of seven such titles, all available for free download via Steam.
DotA 2
DotA 2 is based upon the popular WarCraft III mode DotA (Defense of the Ancients), and it is a strategry multiplayer online battle arena game where you control a hero which can advance through various levels and gain new skills and abilities, buy upgrades, items and have to defeat the enemy heroes and structures. (Image credit)