Actually, playing since I have memories would be too long to list, as you probably.
The easiest way to know me is to visit www.twitch.tv/armazr
If the "tell me your game, I will tell you who you are" exists, then enjoy below biopic.

FPS
COD MW (2007) and some other CODs (such as zombie on CoD WaW).
Some Battlefields
Heroes & Generals (was better before)

Others main
LoL defintely too much (so many account in EUWE, one in EUNE, one in KO)
WoW Mainly (yeah almost only) Rogue from LotK (started on unofficial servers, then blibli got me)
Redstone, uh I mean Minecraft but with mods such as "island block" or "sky factory". Dam you should try if your brain can face it. Nothing about PvP or Vanilla - indeed COD & Battlefield are better sized for it.
Europa Universalis - and I would say any "Paradox Interactive" game is good to give a chance.
Rift (the MMO) in Vanilla mode (monthly payment). Dam man, was one of the best MMORPG. Really the vanilla server was so good. Everything was balanced and soooooooo amazing. WoW is such behind, even now.
Blade & Soul (Korean Game): You just have to try, now it's free.

Others - as just others
Yeah some games were good to play. Because they were famous, or just good...
Half-life, Portal, Dota, All Battlenet games, Tera, Albion, Blade & Soul... the list is too long.

Mobile Game
Yes just to say that the only one game which hold me since years is Clash Royale.