My personal favorite F2P game (and in my top 3 favorite games in general) is Planetside 2.
It may seem like a bit much to get into, but it really is a fantastic game.
There are people that call it pay to win, but they are mostly confusing playtime with money. The types of players that have all the expensive gear have dumped thousands of hours into the game and are just better. Any weapon used by an inexperienced player is going to be just as bad. Also, in game credits are relatively easy to earn, a weapon costing 5 or 10 bucks can be earned in a day or two of good playtime.