Searching Ideas

I've heard great things on the forums about this one.

That aside, any particular genre (dis)preferences?

Are you into game of thrones? I know there is the telltale game out there but you maybe don't know this one:
http://store.steampowered.com/app/208730/

Firewatch is also a good game with much story:
http://store.steampowered.com/app/383870/

Another cool game is Gone Home... Where you come home, but no1 is there. So you have to explore the house
http://store.steampowered.com/app/232430/

If you like or want to give a try to point and click games I like the german company Deadalic Entertainment.
You could start with the Dark Eye and continue with Memoria (the sequel)
http://store.steampowered.com/search/?developer=Daedalic%20Entertainment

..or this one, where you play a cop: (the sequel sucks tho)
http://store.steampowered.com/app/46480/

Also here just like Spec ops a game about war. But point and click and requires uplay:
http://store.steampowered.com/app/260230/

another cool little story is you as guard between to sides of a wall to check the papers. multiple endings and there are also some jokes here and there.
http://store.steampowered.com/app/239030/

If you like more graphic stuff with story the perfect game would be the Story of Ethan Carter:
http://store.steampowered.com/app/258520/

Also if you have Half-Life or another Source game I recomment the mod Underhell
http://underhell.wecreatestuff.com/

hope this is enough for now ( ͡° ͜ʖ ͡°)

To the moon is great , it touched my heart and make every feeling so intensive ... I can't forget about that game , you really should play it. That's my opinion

Personally, I think SWKOTOR has one of the best stories. If you enjoy telltale games, try The Wolf Among Us and/or The Walking Dead games. You might wish to also consider series like Mass Effect, Deus Ex and Bioshock. Brothers - A Tale of Two Sons should have a nice storyline too, but I didn't play it yet. I think everything else I'd have suggester have been already mentioned.

Still Life. It is my favourite point 'n' click, and apparently it was written well enough that people have trouble finding out the identity of the perpetrator. (I honestly have no idea why, I pieced it together back on my first play through, as a teenager.)
Transistor, if you like pseudo-philosophical rumblings and an ending that would probably result in a huge WTF face.
The latest Wolfenstein games have a surprisingly good plot with good action as well, and some segments are quite brutal, almost naturalistic.
The Bioshocks build a decent story on the depths a human would deliberately sink in order to achieve a set of goals… or sometimes the strength of refusing to go there. (I also think the PC controls of the first two have a dreadful aiming mechanic, as if you are constantly struggling against a really overzealous controller aim assist all the time, but it is maybe just me.)

Valiant Hearts: The Great War. You can hardly find anything better than that. Well, if you want, try Bully: Scholarship Edition too, because it's so damn funny. xD

Dishonored - Definitive Edition - maybe when dishonored 2 will be published 11.11.2016 there will be some discount... Dishonored is linear (9 chapters)- but you can play game twice: brutal or peaceful strategy. There are also limited number of abilities you can access- so you can try with different combination. And there are also another character in two dlc's- that sums up to 6 chapters. (And then again 6 chapters with opposite strategy x)

While it's not serious in tone, Undertale is also a great game, where the world feels living, well-built and responsive on it's own way. Also, loads of jokes, puns, and generally extremely witty writing. There's a demo on Steam, you can try it out if it suits your needs :)

Maybe a little different than what you are looking for but I always thought that Alan Wake was an amazing game with a good story behind it.