Yup, some of the F2P games are actually pretty good. If you are into heroes, DCUO is fun and has a pretty good story too.
Warframe is badass and you can play with friends.
Paragon is pretty fun although still in beta.
Tomorrow Children is really good fun I've been told and soon we are getting Let it Die which has got tons of praise.
I know you don't want to pay for online, but one of the best next gen experiences is Destiny. You can pick up Destiny collection for £25 and it has so much content in sp, co-op and mp, it is unmatched. I cannot recommend the game enough especially if you like mp, co-op, rpg elements and need a game that will entertain you for more than a month or two.