Xenogears - My favorite RPG, a little rough in the later acts because of publisher shenanigans, but the story is still good and the gameplay, other than turn based being uncommon now still holds up. (Nier Automata is one of the few more recent games that taps on some of the feelings and concepts Xenogears has in spades)

Worms Armageddon - Less common suggestion, but a fantastically fun game to play with multiple people, even with one controller, since you can pass it around by turn.

Quake 1 - despite my two turn based suggestions FPS is my favorite genre. Quake 1 blends things like lovecraftian and body horror into the environment. And the re-release Bethesda has done is really well done.

Doom 1 + 2 - just for the history lesson. Also has a re-release now that makes it much more playable. Still fun too.

Planescape Torment - You’ll want to be a particular person for this one. I don’t have the patience for isometric rpgs like this one, but the story is great.

Diablo 2 - Pinnacle of isometric action RPG. Wasn’t my cup of tea but if you like the genre, it’ll be a winner.

Day of the Tentacle - point and click adventure, but fun and not quite as obtuse as a lot of them. Will make you think still and the evil tentacle is funny imo. Remaster available on steam too.

Freddy Pharkis Frontier Pharmacist - Another point and click, this one is a selfish add, I mostly add it because I played it a lot and liked it. It may not be the pinnacle of anything, but I found it fun.

Half-Life 1 and 2 - fantastic and fun both. They tap into some things that other FPS still today can’t touch. Really fantastic games.

Vagrant Story - It’s hard. It won’t hold your hand. But it is a good story and interesting leveling/armor/weapon system.

Solstice - NES wizard game. It’s a fun and somewhat difficult dungeon crawler/platformer.

Sonic 1,2,3 - Classics.

Chrono Trigger - Classic RPG

Final Fantasy 6 and 7 - Classic RPGs

Age of Empires / Age of Mythology - Great Real-Time Strategy

Thief - The original games have some clunk to them but they are still fun.

Descent - Probably my favorite 6DOF game.

Heroes of Might and Magic 3 - probably the best of the Heroes games. Good fun turn based adventure game.

The Incredible Machine - A puzzle game where you figure out logical components, I played the Incredible Toon Machine a lot as a kid which is a cartoonish version.

System Shock - Another classic game. I haven’t actually played the original, but am playing the remake. You cN look at both and decide what you’d prefer.

Lemmings - another unique puzzle game. Save the lemmings from themselves, they will walk to their doom.

Yakuza - The series is great and I’d recommend the remakes over the original. Starting on zero isn’t required (It’s a newer prequel) but it’s a good start. The games are all similar in play, so take breaks between them. And the best parts are all the side stories. Seriously, all the fun is there imo. Main story is fun but side stories are more of a draw to me and generally hilarious.

Elder Scrolls III - New TES games are still fun, but they lost a lot of the soul the series had and it gets worse every time. Still fun for what they are, but Morrowind was a unique gem. Fair warning though, it does have it’s rough edges.

A few newer ones because I can’t tell where to cut things off lol:

STALKER - FPS, a bit buggy, but really excellent game. Especially with difficulty mods added. Blends in spookiness, the feeling of being alone, and fun action. Part 2 is set to drop within the next year or so. The invasion of Ukraine has made dev difficult and slower.

FEAR - FPS, this first game is still good fun, the sequels aren’t worth the piss I would take on them.

Mirror’s Edge - The first one is fantastic, just don’t focus on fighting (you’re a runner not a fighter). The first and best First Person Runner game. I replayed it not long ago and still loved it.

Portal - Unique, fun, funny.

Metro 2033 - start of an excellent series. Loved the games, and then the books.

OK I should stop. In general I would suggest playing the remastered versions of any of these games. Many of the originals are victims of their times and did they best they could with what they had while defining what made a game good. The older the game the more likelihood you’ll run into immersion breaking or game ruining designs. We had to tolerate that to find the gems in the rough. You don’t have to do that.