Morrowind. Yes, there are genericisms there, but I still liked the story and especially the way it was told. Also, the way it was not
told, namely the in-game books and dialogue that subtly revealed more about the culture of the Dunmer and the Ashlanders and all that.
Still Life is also pretty interesting. It's technically speaking the second game in a trilogy but there's a reason for the name change. You won't miss much by not playing Post Mortem which is a pretty generic and boring game. A few decades separate the events between the two games, so that helps too. I've heard that Still Life 2 isn't too great, but that's something I have yet to verify myself.
Mass Effect 1 has a good story. The PC port is also well done. Mass Effect 2 has good characters (as does 1) but pretty much no story whatsoever, you're just running around gathering people for whatever the hell happens in ME3. The PC port is atrocious. I would recommend against playing ME2, despite the great MetaScore and all. It's the most disappointing game I've ever played.
Neverwinter Nights 2 is a good game with a too-long beginning. The story is alright but not great, which is mended by the Mask of the Betrayer expansion. Knowing the basics of D&D would help greatly, though, otherwise you might get your ass handed to you because you have no idea what you're doing wrong. Becomes particularly important in MotB when your level will be nudging 40.
Then there's The Witcher and its sequel. This being GOG, you should buy them at some point anyway, so enough of those.
If you're into Doom-era shooters, there's the Marathon trilogy which you can download legally here
. It's a bit like Doom and such, but with a storyline that works properly. Also the first FPS with reloading and dual-wielding.
Also, Grim Fandango, or so I've heard. I'll play it during the summer. Good luck finding a copy, though.
That's two adventure games, three first-person shooters and six RPGs. And about 1000 hours.