There are a number of free to play games (of course, they all have things you can buy, but you don't have to). It depends on what kind of games you like to play. Secret World, Rift, League of Legends...
It would also help to know what you were playing before, so we don't list that one.
I've played mostly RPG games such as Maplestory and Mabinogi (Mabi isn't that boring but I have no friends (I don't know how to make one for some reason). I did play League of Legends and for some reason I can't log in as of today.
If you enjoy mobas in general I strongly recommend Heroes of Newerth. It's the original Dota-port, but it has morphed into its own game with the release of Dota 2 and all. The nature of the game lets you play an infinite amount of games where no game is the same, you get to cooperate/compete with other players and you can play with your friends easily. Or if you prefer a bit more casual setting you could always just make a new account on LoL?
Why don;t you ty free to play games on your PC? It's fun. If you are into First Person Shooters, you are going to Like Planetside 2 for sure. It's a game you can play for free entirely. They are not going to force you to spend any money on ti.
You could try CS:GO, I know it's not free, but after playing for a while it will buy itself off, because you get drops in-game, which you can sell for steam wallet or trade to paypal. I do not recommend the latter as it's dangerous and you could get scammed.
Do you like plane and tank combat? Check out War Thunder. It's a free to play game, and it's available on Steam. There are five available countries, USA, Germany, Russia, Great Britain and Japan, and you can choose whichever you like. You can either fly a plane or drive a tank. By completing a match, either winning or losing, you earn in-game currency, which you can spend for researching new weapons, better armor and, basically upgrading your vehicle. It's a fun little game, and best of all, it's free to play. Check it out if you are interested in these kinds of games.
If you like rogue-like games I would recommend the Binding of Isaac. It is not free, but often is on steam sale, just costs ~5€ all the tame and honestly it is great fun.
In case you are more into the MMOFPS genre I recommend Planet Side 2. It offers fun gameplay and great graphics, I did enjoy it for a long time. Giving it a try can't hurt since it is F2P.