I'll go first:
Team Fortress 2:
This game has been around for a while. I guess I like it because of it's movement mechanics (rocket jumping etc) as well as general silliness. It also focuses on the whole "team" thing quite well. It's just good fun and is my most played game. It seems to have a very very highj skill ceiling. (please remove random crits and actually update the game Valve!)
Has no relevance to my username what so ever. I'm bad at putting things in words, but this game tells a very beautiful story and I recomend you play it.
The life is strange series:
Love the story, don't want to spoil it. I haven't played LiS2 due to the inclusion of denuvo. I might grab a pirated copy when the last episode is released. Or pay if they choose to remove denuvo. Either or.
Just Cause 2&3:
Boom! explosions and stupid physics are fun. Not much more to say here. (JC4 was bad though)
Very philosophical and deep story, fun combat and 2b's butt. Bring tissues (for two purposes). I must get around to playing the original NieR
Mario Kart Wii:
What can I say, it's mario kart. Fun as fuck and I can emulate it with Dolphin on my phone and computer.
Brilliant puzzles which are fun to solve, brilliant characters and story. And it's cheap.
I have followed this one since quite early in it's developement. And I hightly recomend you play it. It's a survival horror crafty thing. And it actually has a plot.
I haven't actually finished playing this one, but so far it has been pretty fun. It is ridiculous and seems to be quite self aware. But just because all of Bayonetta's clothes fly off ironically doesn't mean someone isn't still stroking their sausage to it.
the fanbase ruins this one unfortunately. But it doesn't change how good the plot is.
dewm (doom 2016):
Original doom is good. This one is also.
And some "classics" include Tetris, Minesweeper, commander keen, Duke nukem 3d and super Mario 64.