Now there are games I have not played so there may be some left you find interesting, but here's some games I can vouch for.

tf2 (classic class based team fps)
dota2 (good moba) "league of legends isn't bad ether"
warframe (3rd person space ninja game has gun play and melee a bit of a grind has rpg elements)
robo craft (a vehicle creating game where you make a vehicle to fight and do objectives in game modes)
dragons nest (mmorpg not dead what ever story but is one of the more action oriented play styles) "tera looks fun but havn't played it"

relic hunters (top down isometric shoot em up game)
hawken ( class bassed mecha)
spookys house of jumpscares (a cute horror game)

Let me know any f2p games you recommend or if you dissagree with me.