Free to Play games are growing like mushrooms after the rain. Free to play essentially means that you can just install the game and play it without paying any money. You have a choice to buy some cosmetic or some other utility items from the ingame shop and support the devs, or you don't have to and just enjoy the game without paying anything. Nobody will hate you for it. I personally never buy skins because I came from the era of gaming where skins were always free, just remember Half Life multiplayer games where you could freely chose any skin you wish and go into the match. Today skins are behind paywall and let them have it. There are quite a lot of Free to Play games on the market today and here are some of the best ones.
Dota 2
Dota started as a mod and is now fighting with League of Legends for the 1st place of the most played game on the planet that is also a free to play in it's monetary concept. Most of the moba games are Free to Play and in this one you can buy many cosmetic items if you wish.
League of Legends
Another popular Free to Play moba is for sure League of Legends, everyone played this game at one point in time. This game is truly huge, it is a top payed Esport today with millions of dollars in prize money. But as a normal player you can just install it and enjoy it without spending a dime, if you wish buy a skin or two to support the devs and that's it.
Marvel Heroes 2016
Let's switch from Free to Play mobas to MMOARPG. Marvel Heroes 2016. is a game that will surprise you how deep it is considering it is just about Marvel comic book superheroes. You can spend money in game to unlock heroes faster and to collect some good looking costumes. There is an ever expanding roster of heroes in the game with 60 heroes playable at this moment.
Hearthstone
Popular Blizzard card game is one of the best free to play games on the market. You can unlock every card just by playing the game and completing daily quests. Slowly but surely you will get that Ragnaros or Sylvanas to complete your mighty deck. You can also buy the card packs for money if you are impatient.
Evolve
This is a Free to Play multiplayer game where 4 players hunt monster that is also controlled by one player. Monster can evolve into 3 stages and each one is stronger. Hunters have special sets of weapons trying to counter the monster and track it down. Fun concept and the game is Free to Play on Steam so give it a shot.