Hi everybody,
I am just wondering which GoGs have great story. Story so great that it will actually leave a mark on you or simply great story :). To give examples games which I though had great story :
Beyond good and evil
Darkness (PS3
Portal 2
Half life series
Baldurs gate series
Realms of haunting
Planescape torment
The longest journey
Fallout 2
Bioshock 1,2
Witcher
Deus ex
Mass effect series
Dragon age series

I'd recommend Sanitarium.

Teenagent. It pulls satire off quite well, without coming off as trying too hard.

Then there's also Beneath a Steel Sky.

Gabriel Knight is my recommendation.

Betrayal at Krondor has a great story, and I can attest to this.
Return to Krondor is said to have a very good one, too, but I haven't really played that, so I can't say anything about it. (I read Tear of the Gods, the novel based on Return to Krondor, and was pleased with it, but I don't know much about the story of the game proper.)

Additionally, I liked the story of both of the original Fallouts very much (not only that of the second game), and also, that of Arcanum; I think all three of them are well-written, with highly memorable places, events and characters.

Here's what I've seen unsaid

King's Quest 6
Divinity 2 Dragon Knight Saga

everything else has been posted that I would suggest

Probably an unconventional choice for a great story thread because it's something entirely different than e.g. the wordy (and ingenious) Planescape Torment but I really like the story-telling in Psychonauts, too. The story itself is a bunch of baloneys but lots of fun, full of laughs, suprises, weird and lovable characters. And you can witness several side-stories if you explore and observe what's going on around you. There's also this neat feature that you can discover little slideshows inside people's minds that tell their tragic stories in pictures, without words.

So if Beyond Good & Evil and Giants: Citizen Kabuto are already on the list, Psychonauts should be, too. :)

I second both Arcanum and Beneath a Steel Sky.

Also, although I didn't finish the game, from what I saw of Septerra Core: Legacy of the Creator, it had a good story. Again, though, I didn't finish the game.

Outcast if you like StarGate

Betrayal at Krondor if you like fantasy

Beyond good and evil if you like conspiracy

Original War if you like RTS

The Longest Journey if you like adventure

Just ask away about whatever for details

edit: Oh, I totally forgot they have The Witcher now! The Witcher if you like Amazing!

Seconded on Sanitarium

Would include the Gabriel Knight Games and the Tex Murphy series, Fallout Series.

I'm sure there are others, these are my favorites.

Painkiller had the best story of all time
...
... Well.....no, not really.

However I found I quite liked the story in Another world, nothing was said, but I remember feeling really sad at the ending nontheless. Great example of building mute character personality.

If you like comic book stories I really liked Freedom force. Never tried the 3rd reich one, but if it's like the first one in storytelling it's a great homage/satire of classic superhero comics. Not the most coherent or involved plots, but the art style, sound bits and presentation worked really well for me.

Broken Sword games
Gabriel Knight series
Police Quest 1-3
Still Life
Tex Murphy games

If you like point 'n' click adventures, you really can't go wrong with these:

Gabriel Knight 1-3 - you really, really should try these if you enjoy a good story and dialogue. The GK series have some of the (if not the) best writing in games ever. You can really see that they were created by someone who is experienced in that area.

The Last Express - an exceptionally mature (as in grown-up and believable) adventure game and a gripping mystery story to boot. I haven't finished this one yet, thought, because of the somewhat frustrating gameplay, so I can't comment whether it ends as well as it starts.

Syberia 1-2 - the two Syberia games have a melancholic athmosphere that is very rare find in games. I just wish the games had a way to skip the walking animations and had less illogical puzzles, because now they were a bit of a chore to play through. In the end, I perseverd, 'cause I wanted to see the conclusion of the story.

And if you haven't played the first Fallout, you should. It's as good as the first one.

Hope you enjoy these!

I agree it has a neat story (maybe not as great as that of some others listed here, it's still more of an ARPG after all, but very memorable, especially regarding the characters involved), too bad it's not on GOG, thus doesn't comply with the thread title.
Anyway, I'm playing it through for the second time right now, in quick succession, it's that good as a game :-).
(OK, I'll stop derailing the thread now.)