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Brothers - A Tale of Two Sons

I don't know if that is considered cheap but it goes very cheap during sales so if you wait for the winter sale it is a great game, not too long and a great story.

Ryse: Son of Rome has a really cool story. It's a great game, especially if you're interested in the roman era. It goes on sale for 5 bucks pretty often I think. The only downside is that it gets a bit repetitive after a while.

If you enjoy GTA games, GTA San Andreas' story is really good. It's getting quite old now, but I'd say it's still worth playing.

The Wolf Among Us, Tales From The Borderlands

Most of the Daedalic Entertainment games. Valiant Hearts and Bully too.

Life is strange.

Look for a thread from a week or so ago filled with point and click game recommendations. There should be something for you there.

Other Telltale games are great - Tales From The Borderlands and The Wolf Among Us.

Other decision-based: Life Is Strange, D4: Dark Dreams Don't Die.

Cave Story +, To The Moon

Brothers: A Tale of Two Sons: Really short, but amazing game.

FPS with good stories: Usually around 10 hours. Metro 2033 and Last Light Redux, All the Bioshock's, Wolfenstein: The New Order and The Old Blood, Far Cry 3, Amnesia: The Dark Descent (horror)

Between Me and The Night
Contrast
Deadlight
Dear Esther
Event[0]
Inside
Lumino City
Papo & Yo
Planet of the Eyes
Stick It To The Man!
The Darkness II
The Fall
The Silent Age
The Turing Test

Man, you should play Firewatch! Short (4-6 hours) and excellent story.

deponia 1-4

To The Moon is my favorite!

ori and the blind forest haven't played it but hear it's really good
Undertale
Brothers:a tale of two sons see first post
Bastion is fucking amazing
Never alone
if you want to message me on steam I can probably suggest others and ways to get them

Spec Ops: The Line.

It has the best story ever

Magicka! for the lolz!

Transistor!

Brothers - A Tale of Two Sons
Dust: An Elysian Tail
The Longest Journey
The Cat Lady
Mafia 2
The Banner Saga
The Whispered World
Still Life
Gone Home
To the Moon
A Bird Story
Spec Ops: The Line

A Bird Story is very short.
Brothers, Gone Home, To The Moon, and Spec Ops are medium length.
The rest are longer.

Brink of Consciousness, both games.

D4 dark dreams don't die

Firewatch (I do really love this game, good story, great emotions, not much gameplay, a shame that you have watched the story, DON'T DO THAT!)
Oxenfree (I am playing that right now, it is not great but still good, great art, great soundtrack, ok gameplay)
The Vanishing of Ethan Carter (will play that next, not played yet)

Some people here won't agree with me, but imho Portal games are true masterpieces.

Bioshock if you like shooting and using powers.
Great story, especially Bioshock Infinite which references part 1 a lot.

Oxenfree. I loved it. The story is quite nice (I think it's better to play it completely blind, so I won't say anything about what's it about) and I loved the way the conversations flow and the way characters react to what you say (or don't, as you can play the entire game without saying a word).

Are you into point and click games? I've recently finished The Inner World and it was pretty cool

Spec Ops: The Line
Maybe its story is not that great compared with other story-rich games, but it is thought provoking after finishing.
Playing time varies based on which difficulty you choose. First run Suicide Mission and about seven hours for me.