Games with exceptional writing.

[JoeQ]

The GTA games from Vice City onward. No, really, those games have excellent writing, especially when they go full crime-comedy.

[phediuk]

Traffic Department 2192.

1994 DOS shmup with exceptionally dense plot and large cast of characters; the cutscenes are longer than the levels and are the main attraction of the game. I played the shareware version over and over back in the day; it had the whole first episode (20 levels!), it was like reading a novel with some game parts in between.

[Snake]

I'm sure I've mentioned it elsewhere before, but "Return to Zork."

There are quite a bit of interesting scenarios that is written into vocal dialogue and interaction.

For example, if you pick up a piece of raw steak.  After a while, the raw steak in your inventory will become rotting steak.  So as you interact with the townsfolk, they'll notice. And it's all done with pre-recorded FMV or live voice acting.  So the blacksmith will be working.  As you arrive, a live cut scene will have the blacksmith sniff around, sniff his armpits, then sniff at you. Then he'll tell you, "You stink!"   

There's a lot of humorous quirks and details in Return to Zork. All so memorable.  

[Maciej Miszczyk]

Planescape: Torment, obviously. Chris Avellone has to be the best writer in games
Fallen London/Sunless Sea have great writing too, I see where people are coming from when they say that Alexis Kennedy might be current generation's Avellone, even though the game he worked on would benefit from a better designer
Pathologic is another game that comes to mind - the first translation might not have been that good but dialog in the 'Classic HD' version is just great
Spider and Web is probably the best use of unreliable narration in video games, and it actually uses that for a really good puzzle
What Remains of Edith Finch, but I might be biased because it just does a lot of the things I like: it really gets me with its melancholic magical realism, it does that thing in which different characters have different writing styles associated with them and it manages to tell a good story while having many of its parts composed of references and quotes
King of Dragon Pass is great at mythological stylization - fantasy games might have 'deep lore', but it's probably the only time it felt like reading actual myths
OFF might be better known for visual style and atmosphere and to be honest it's probably the weakest one on the list when it comes to pure writing but it's occasionally brilliant in a very quotable way