Game you played with the best storyline?

Dragon Quest V.

Dragon Quest VIII and Suikoden V (I missed the previous ones, unfortunately.)
Edit: Oh, and Heavy Rain and the Mass Effect series.

Both KOTOR games, Indigo Prophecy (Fahrenheit), both Witcher games, Mafia 1, Vietcong, Fable, Call of Juarez, Shadowrun: Dragonfall, Brothers: A Tale of Two Sons, The Saboteur, Alan Wake, Bioshock, Sleeping Dogs.
The Wolf Among Us and TWD, obviously. And obligatory Planescape: Torment mention. (but I never quite liked its taste)

Mass Effect, Dragon Age and Neverwinter Nights 2 may not have the most mindblowing or original stories, but it's the narration and immersion that make them great story games.

It's too hard for me to choose THE game with THE story. :|

Digging in my memories, I can say the following that I've played:

The Legend of Zelda Saga (Especially Ocarina of Time and Majora's Mask) | Warcraft III: Reign of Chaos + Frozen Throne | Mafia | Legacy of Kain: Soul Reaver | MediEvil (Both 1 and II) | Oddworld: Abe's Exoddus | TimeSplitters Saga | Dust: An Elysian Tail | Brutal Legend

Tomb Raider

Enslaved

Mafia: City of Lost Heaven

Fallout 3, Faringeit and Crysis 2

Assassins Creed( the first ones aka Ezio)
Prince of Persia Sands of time
Saints Row series, love the ridiculousness

Call of Duty Multiplayer C:

Lets see...

• Enslaved (Ninja Theory is awesome and the characters had great chemistry)
• Eternal Darkness (One fucked up crazy horror game)
• Last of Us
• Bioshock 1 and Infinite
• Advent Rising (Too bad it'll never be finished)

I know there are a few others which one I can't think of and it's really bothering me. It actually pulled the heart strings pretty good.

Tales of Graces F , Tales of Symphonia , Tales of Symphonia Dawn of the new world

Witcher 1

Deus Ex 1 from 2000, and Max Payne 1.

Metro series, Binary Domain, Brothers in Arms, Gothic 1-2, Kotor 1, Vampire the Masquerade (and maybe Banner saga)

Dota2 very brief and interesting storyline

Dota2 very brief and interesting storyline

Grandia 2

Half-Life and Dead Space

Bioshock series, Mass effect series, first and second Gothic, Alan Wake, To the moon, Deus ex: Human revolution, Spec ops: The line, The Last of Us, The Witcher and The Witcher 2: Assassins of Kings, Assassins creed 2, Mafia: The City of Lost Heaven, Metro 2033 and Metro Last Light, Star Wars: Knights of the Old republic

Fallout
Metro serie
The longest journey
The early Resident evil games.
Half life serie.
F.E.A.R serie.

All i can think of right now.

The Walking Dead

The Wolf Among Us was nice. :)

Fallout 1 & 2