Old games are generally my favorite games so you've got quite the link dump incoming:
Gothic - Eurojank medieval-fantasy RPG with an incredible story. (needs mods to be playable without issues)
Gothic II - The superior followup to what was already one of the greatest games ever made, now with a little less jank. (also needs mods to be playable without issues)
most mods for the Gothic games can be found here
Risen - Gothic, but now you're a pirate.
Thief 2: The Metal Age - Sneaky boy takes all the stuff.
S.T.A.L.K.E.R. Shadow of Chernobyl - A normal day in the life of a Slav.
S.T.A.L.K.E.R. Call of Pripyat - Gopnik Simulator 2
Betrayal in Antara (might be abandonware at this point; no Steam or GOG link to be found)
Fallout 2 - If you don't know what this is you probably haven't played a game since the Commodore 64.
Omikron: The Nomad Soul - David Bowie did the soundtrack. Think about the game that David Bowie would do the soundtrack to and you're probably pretty close.
Pathologic - A mysterious disease is killing everyone in a small town full of inbred sociopaths and you're trying to cure it, but actually nah.
POSTAL 2 - Brendon Tarrant simulator with less memes.
Star Wars KOTOR II: The Sith Lords (mods that restore all the cut content are necessary, but once properly set up is far superior to the original game)
Strife - If someone were to make a Doom mod and turn it into a proto-fpsrpg, but it was actually really good.
System Shock 2 - It's the future, there's a murderous A.I., you have psychic powers and a shotgun.
Blade of Darkness - The original soulsborne before Demon Souls was even a thought. (abandonware)
E.Y.E: Divine Cybermancy - Oddball FPS with crazy guns. You won't really understand what's going on, but who cares, you gain brouzouf.
Deadly Premonition - If Silent Hill was a game by David Lynch in an alternate universe where he's Japanese. (don't know if this one can really be considered "old" per se, but it's definitely a cult-classic)
Puzzle Agent - Weird adventure game full of fun and varied puzzles, good style and murderous garden gnomes.
Uru - The mostly unknown follow up to Myst and Riven. They went full 3D third-person with this one though and is in my opinion way more interesting than its source material.
Arcanum: Of Steamworks and Magick Obscura - Shitty title, excellent rpg. Has a pretty unique setting as far as videogames go with its "Victorian-Steampunk" aesthetic, but pulls it off without seeming like it was made by a bunch of weebs who are way too interested in corsets and cogs.
Arx Fatalis - Arkane Studios underground precursor to the Dishonored series, but with more actual roleplaying elements and a cool magic system.
Vampire the Masquerade: Bloodlines - Relive your gothic fruitcake glory-days with this edgy vampire rpg. It's way better than I make it sound here, but definitely still has a little tinge of cringe to it. (absolutely needs mods to be playable as it was released half-finished at the tail-end of the life of one of the greatest studios of all time Troika; get the unofficial patch and clan quest mod and you'll have a couple hundred hours of fun with this one)
There are an absolute ton of other games I could list here, but this is already pretty long and I'm getting a headache, so I'll have to follow this up with a part 2 sometime later.
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