Battlefield 4 for PC (if your PC can run it)
AMAZING GAME.
Battlefield 4 is shit, Battlefield 3 is way better.
League of Legends. You won't regret it.
LoL is only fun drunk, at least for me.
Bump ^-^ starbound any good?
Starbound is pretty good. Just like Minecraft/Terraria but with a ship to travel to other worlds.
Borderlands 2 , Dead Space series
Borderlands 2 is good.
Dead Frontier is a f2p browser-based survival horror MMORPG. You said you aren't a fan of zombie games but you played one you liked. So, I am still recommending this one.
Neverwinter is a f2p mmo D&D game. I have developed a love/hate relationship with this one. It's the one game that I ragequit but I still keep f-ing playing it from time to time.
Aion: Ascension is a decent f2p MMORPG.
Fiesta Online is a f2p 3D cartoon style MMORPG.
Ragnarok Online is a f2p 3D fantasy MMORPG based on Norse mythology inspired by an anime.
Jade Dynasty is a f2p martial arts inspired 3D MMORPG. Personally, this one is my fav of the ones I listed.
RUST is on Steam. It's a cross between Minecraft and DayZ. As a starter, I recommend beginning on a less populated server until you get the gist on the game.
Path of Exile is a 3D Action RPG. It's what Diablo 3 should've been like.
World of Warcraft is pretty self explained since it's been around a long time.
(One of my long time favorite games until the release of Cataclysm & then I rejoined in the last few weeks.)
Eve Online is a sci-fi MMO & has a 14 day free trial period. It has a long learning curve. (One of my long time favorite games.)
These are just to name a few off the top of my head.