Spec Ops: the Line. The story is simply unforgettable.

Warcraft 3 and the Frozen Throne expansion, while very old by now, have amazing storytelling. Arthas' fall, the orcs' second round of corruption and attempt at redemption, the night elves getting their shit wrecked by everyone and fighting back. It's easy to see why so many people got hyped for World of Warcraft back then.

Another old game that is totally worth it for the story is Soul Reaver, which received a remaster last year. The voice acting alone carries the game, it's a tale of hate fueled revenge with Shakespearean dialogue. The downside is that you can't skip cutscenes (this used to be a real bother back when you had specific places to save, dunno how it is on the remaster)

Lastly, Elder Scrolls 3 Morrowind. If you can get past the jank, or mod some of it away, and follow the main story, you'll be surprised at how much thought went into the world building of the game. You can use OpenMW to also get rid of some bugs and have an overall better technical experience with the game (better resolution and graphics options, almost zero chance of crashes, better support for current systems)