In the literary world, anyone writing a masterpiece before they're 40 is heralded as a genius. The video game industry sucks them in young and spits them out barely any older. Those who survive past 40 (and who can influence the story) are usually famous designers who are valued for their technical design and project management skills, despite how much they wax philosophical to the gaming press, and publisher execs.
Some studios have built a reputation around storytelling (looking at you, Bioware), but haven't actually produced an original story for years. To pick on Bioware again (they're a great example), they have become very, very slick at telling that story in lots of different settings. They've become very good at using a combination of cinematic direction and emotional attachment to draw you into the story. Technically, they're doing a good job of telling the story better. The story still stinks. I say that as a fan of the Mass Effect series.
I think it might seem like the story has gotten worse, but the truth is that it was always bad. A story always seems better the first time you hear it and, as we gain age and experience, we develop in our level of sophistication and appreciation. It's natural.
I'm not tarring every video game story with the same brush - there are some good ones out there. It's hard to find both an original story AND an original setting, though.
To answer the question: probably Grim Fandango. I have enjoyed several since then (notably The Witcher and Mafia), but Grim Fandango was simply unique (for me).
damn, almost forgot! Culpa Innata, now that was an awesome game!
I found the game part clumsy (as an adventure game fan), but the setting and story definitely drew me in. I managed to get within minutes of the ending only to have a bug stop me. In the first few hours of the game I didn't complete a neccessary task, but the game let me progress anyway. Still haven't seen the ending - maybe one day I'll have lost enough frustration to attempt another playthrough.
But yeah, good call!