Dark Souls (Entire Franchise) - Probably my favorite franchise. Great combat, amazing story, and so many different options just keep making me replay the games.
Cave Story - One of the best indie games ever in my eyes. An amazing story, fun platforming and fighting, and tons of challenges you can do for yourself. Speedrunning this is also really fun.
Town of Salem - It's mafia, put in a browser. Still one of the best deception games ever, and it's free to boot. Seriously, give this a try if you like mafia at all. (Although I might be biased here because I do mod /r/townofsalemgame)
Counter-Strike: Global Offensive - One of the most played games for me in recent times. The game requires a ton of skill to get good at, and for someone like me who likes to improve, this is great. I like how the game pretty much says "5 people on each team, this team attacks, this team defends, here's the timer, go." It throws you in quickly round after round, without it being dull in any way since you can play it differently each time. Currently sitting around SEM with 96~ wins.
Other things to mention: Smash, TF2, Ace Attorney franchise, Risk of Rain, Nuclear Throne, Crypt of the NecroDancer, Borderlands 2, Terraria, Realm of the Mad God.