Hearthpwn

I second Life is Strange. It's all story and certainly fits under a indie game label. Plus it's worth playing for the art and music alone.

Limbo is very cool made. But they never tell you anything about the story so you can only guess and the ending man....the ending almost destroys the game. The game is such amazing in the begining and i really recommend it but jesus christ. THE GOD DAMN ENDING IS THE WORST ENDING IN GAMING HISTORY. If u hate bad indie game endings, dont go near this game...

the Dragon Age saga before Inquisition has a pretty amazing story, Inquisition is just a cash grab tbh, but the first two games are really amazing and engaging.

Also i really don't own the game but have been able to watch a lot of it when my friend was playing it and Dishonored is pretty damn sweet.

Also the Snes shadowrun videogame is amazing as well, they didn't do it enough justice with shadowrun returns but it has a cool story as well. 

Overlord and overlord 2 are totally recommended, it's more in the humorous side and you Play as the main villain trying to subjugate the world of the story so the ending is kinda up to your perspective. 

Clive Barker's Undying

Enslaved: Odyssey to the West (PS3, X360,PC), Bravely Defaul/ Bravely Second: End Layer (3DS), Heavy Rain (PS3), Telltale's The Walking Dead Season 1&2 (Pretty much everywhere xD), Uncharted Franchise (PS3-4), The Last of US (PS3-4) and Assassin's Creed II - Brotherhood- Revelations (Ezio Saga)

Chrono Trigger

Ib, Mad Father, Yume Nikki, The Witch House, OFF, Mogeko Castle, Wadanohara and the blue sea. Those are all good indie rpg maker games that everyone should play

If you're up for a game with a story that would take some effort to find Don't Starve is one of the best.

Baldur's gate. mainly shadows of amn, the second one.

Along the same lines that Braid has a very light yet poignant story, I would strongly suggest Shadow of the Colossus. It's my absolute favorite game, and features a story very delicately woven into a relatively barren environment, combined with great gameplay... like Braid!

For other recommendations, FF10 and Chrono Trigger are up there for me in regards to story. And if you want to see how NOT to write story, play FF8 :)

If I would have to recommend a game mainly for it's story, it would be Final Fantasy 9, it's great.

Ico, Shadow of the Colossuss and Metal Gear Solid 3.

Resident Evil 4 is one my favorites purely gameplay wise though if you can stand a campy Capcom story.

I can't recommend  outer wilds (not worlds) enough . Great space exploration puzzle. It's a simple game, but really engaging. It's fun uncovering the mystery of the past, while exploring some really unique planet . Also, you'll die a lot. 

I also second life is strange. That game stuck with me for a while after I finished it  

Quote from Savvyaeu >>

TO THE MOON- PLAY IT OR REGRET IT !

This thread is 4 years old my dude

I'd recommend Tales of Berseria, easily a 44hours long campaing and, excepting for Velvet, the main cast are pretty much Anti-heroes done right, pretty much none of them are the cliched gritty loner edgelord sitting in a corner critisicizing the party and refusing to have ny semblance basic communication, well Velvet is at the start of the story, but the rest of the cast is super interesting and the story is very engaging.

edit: sorry, i got necrofished, didn't see the guy was replying to a 4yo thread 

Portal 2

Witcher 3

I don't know if you're into slow-paced, walking simulator games, but these are the games that made me have the best mind-blowing experiences. Life is strange is one of the most popular ones and I totally fell for it too. I'd say Everybody's gone to the rapture was to me the deepest. I never played Firewatch but all my sources agree to say it's also one of the best.

Triple A narrative games like those from Quantic dream are to be considered, especially Heavy Rain.
Bioshock's my favorite script ever, amazingly tied together.
I second Enslaved: Odyssey to the west.
Her Story if you want to try out something where the smart gameplay is intertwined with the smart story.

Goddamn it. Them Priests always play Ressurect into "the ancient thread" 

So fucking lucky dude