To tell the truth, there are very,
very few truly-"Free" F2P games out there. Most find some way of suckering you into tipping your wallet into their bank accounts. There are a few that actually follow the philosophy, but not many
I used to frequent this game called
Rusty Hearts for a while, until I came back after a hiatus only to find that the game was stuck in permanent limbo =_=
If you're the action-y type, and don't mind a lot of platforming,
Elsword Online is pretty fun, although it's hard to get into the economy when even decent equipment can cost you millions, and the free shops only have three spaces... Though last time I looked they changed things around with the skill system, and haven't been able to play since. However, be aware that you likely
will be dropping money if you want to get far -- a second four-slot skill bar is still locked behind a 9$ pay-wall last I checked, and you will need it if you want to survive higher levels :<
Another one I've gotten into is
Path of Exile, which is actually a Western MMO, for once o: It's your basic
Diablo look-a-like, but different in that leveling up gives you access to new passive skills, and your active skills are placed on your equipment via gems (ala Matera from FF7). However, how you build your character is up to you. Want a spell-slinging Ranger? Or perhaps a Witch with a penchant for cursing enemies before beating them senseless? You can do it, and if you know how, it can be a viable class in its own right.
Also, the game has quite a bit of challenge, without being overwhelmingly "hardcore" (ie- making the game impossible to win except by trial-and-error). It's really fun, even solo :3 Dungeons are also single-instance affairs, so no one can waltz in and steal your hard-fought goodies.
Perhaps best of all, there's no "pay to win" mindset in the game; the best items are found within the game, and stuff in the cash shop are all for looks. No random lotto or gachapon games, no overpowered crap hidden behind a pay-wall, no blocked content; everything you'll ever need to play is in the game itself!
Last one here (for now): if you're big on FPS multiplayer but need one with a sense of humor,
Loadout is your game. Every weapon is customizable.
Every. Single. One. A pulse rifle that shoots rockets? Done. Rocket launcher that shoots lasers? Easily! Shotty that lays mines everywhere? Piece of cake. It almost has a
Borderlands feel to it, without the equipment farming and "we want your money, buy our DLC or else" feel. As well as public and private matches, there's the usual array of deathmatch/CTF/king of the hill/and so on. They're even adding a campaign mode with cooperative play soon ^_^
The only downside I can think of is that, if you aren't particularly good at shooters, it can take a while to get the better weapons. Also, the game is gloriously bloody, so if that's a problem... well, ehh. XD Not sure about the cash shop, but I haven't really heard negative stuff about it.