Games with good stories ?

Brothers - A Tale Of Two Sons
Far Cry 3 (or 4 but 3 is better imo)
Thomas Was Alone
The Walking Dead
Life Is Strange (but wait until the 20th to play when episode 5 is released) <3

If you're looking for amazing stories then you must play Max Payne 1 & 2 and Mafia 1

Heavy Rain or Shadows of the Colossus (more visual/environmental storytelling, but still great), and second to whoever suggested the batman arkham series.

And the deponia series is on humble bundle right now for $7+ for all 3, decent story so far from a point and click comedy angle.

The Witcher 2
Wolf Among Us
Bad Rats
HuniePop

The deponia series is awesome except the end, which leave a bitter taste in your mouth. For me it ruined the complete story (like 80% of all other players).

1. TellTale Game of Thrones
2. Crusader Kings 2 : Way of Life
3. Neverwinter Nights 2 + expansion
4. Mass Effect 1,2,3

Alan Wake
Valkyria Chronicles
Castlevania - Lords of Shadow 1
Transformers: Fall of Cybertron
The Evil Within
Remember Me

I actually liked bioshock infinite a lot,make sure to play the dlcs.

Metro 2033 and Metro Last Light, I myself enjoyed the story very very much until the very end of the games. If you haven't already I advise you to check them out, tho I'm not sure if there is a french language :P
Also Mafia 2 is a gem, the story is insanely good, I've completed the game like 5-7 times :D

Life is Strange
To The Moon
BioShock Infinite
Dark Eye - Chains of Satinav + Memoria (especially Memoria, and it's also possible to play only this one)
Telltale Games (Walking Dead, The Wolf Among Us...)
The Beginner's Guide (this is an unconventional one, but i love it)
Enslaved

Hmm, I've noticed most of my usual choices for story haven't been listed

Star Wars: Knights of the Old Republic
Fairy Fencer F
Hyperdimension Neptunia

I know this is SteamGifts, but you never specified a platform. Are we limited to PC? If not, some of my favourite games are in the Tales series of games, due to their story. I'd highly recommend taking a look at them, aside from Tales of Xillia 2. If you're looking for a good story, they're definitely the go-to.

Edna & Harvey: The Breakout and the sequel have much in common with Deponia.