Grand Theft Auto(owned and going to do this in FPS mode if I get around to it)
Souls/Bloodborne(own at least one of these)
Uncharted/Last of Us
Word Of Warcraft
Call Of Duty/Battlefield
Minecraft
To name a few of the big ones.
Plus some others like Sonic, Mortal Kombat/Streetfighter and Pokemon which I haven't played for over 20 years.
Here's a list to give you some idea of what "big" is:
https://en.wikipedia.org/wiki/List_of_best-selling_video_game_franchises
I've never played any game or series in which multi-player was the primary mode. I've tried two Final Fantasy games and never gotten far. I've tried two Fallout games and didn't get far.
I've played far too many hours of Mass Effect and Dragon Age, and thanks to EA I may never play another one.
Up until a few months ago, my answer would be the Elder Scrolls series. Never played one until I got a huge urge to play an RPG and bought Morrowind off of GoG. I'm shocked how good of a game it actually is. If you can get past the horribly dated inventory system and you install a few mods to modernize it, then it's a gem to play
Just a warning about first person in GTA. It makes me feel violently ill after looking at the screen for a few minutes. The frame rate drops on console in first person, and there's something about the camera movement that does not agree with me at all. Red Dead is similar, but they made FOV adjustable on console so it is not as bad. I still play in third person though.
I never get motion sickness from games so I should be good my monitor is 24 inches and I don't like my gaming TV's bigger than 40 inch so maybe that helps. I think I'll need an Ironsights mod
I never play Mortal Kombat/Streetfighter style side view fighters. I used to play COD/halo and iracing/car games when I had a steering wheel a few years back. Recently I play civ or fallout.
Looking at the lists it would be easier to mention the ones I have played than list out the ones I haven't.