I ADORE Psychonauts and it's writing is, like 80% of why. It's a really well-done coming-of-age story and a ridiculous cartoon and a thorough exploration of being autistic in a neurotypical society all at once. I wrote a whole page about it for my website here, if anyone is interested.
I also really dig all kindsa point-and-click adventure games, which tend to be really story-oriented. Broken Age, Grim Fandango, Edna and Harvey, and Day of the Tentacle are all ones I've played so far and enjoyed. I'm really excited for the game Prim which is still in development but looks like it'll be really good.
I'm always looking for more story-oriented games! Would love to see other people's recommendations.