I seem to remember that there was a German version of this game released a couple of years ago which unlike the original supported anti-aliasing (http://www.mobygames.com/game/longest-journey-special-edition). Does the gog.com version include that feature?

From what I remember from back in the day, you could get anti-aliasing in the normal English version as well. If you had a GeForce graphics card you could enable both anti-aliasing and anisotropic filtering from the nVidia control panel, but the equivalent maneuver did not work for ATI Radeon cards. Someone created a community patch that fixed the ATI problem, but it only worked for the English 4-CD release. (The download version of TLJ is derived from a later 2-CD/DVD reissue)
This was years ago, and the ATI problem (believed to be a problem with the Radeon software, not with the game) may have been fixed. Go to your nVidia/ATI control panel and try to enable AA+AF. Seeing as the games runs in 640x480 resolution, it really makes a difference!

I have the special edition of Dreamfall, which was released in the UK. It contains the DVD version of TLJ, and I also have a GeForce card...
However, AA just screws up the game. It has a very strange engine which is part 2D with 3D sprites. If I enable AA, you can tell, from the prologue there are graphical errors. They first appear when you look at the tree. The top of the tree does not appear untill you start talking to the tree, then it flickers.
I have a GeForce 8700M GT, with SLI and drivers 190.62.
I have tried all drivers from 17x.xx onward, and various SLI settings enabled/disabled. If anybody has any other ideas on what I can try to get AA to work, please let me know :D

I am having the same problem with antialiasing on a GeForce and recent drivers :(
I distinctly remember that a few years back FSAA was working fine in DVD version (which I am assuming GoG version is based on) on an nVidia card.
I hoped that GoG version will not have any problem with FSAA, as it really really helps to improve graphics - using nHancer I forced supersamping AA and the result was a noticable improvement.
No AA:
http://img508.imageshack.us/img508/1372/tljnoaa.png
Supersampling:
http://img199.imageshack.us/img199/3478/tljaa.png

I can confirm that forcing AA screws the game on Radeons as well. You need to restart TLJ for the changes to take place but when they do it is a mess:
http://www.bankfotek.pl/image/395294.jpeg
April's model is silky smooth ( <3 ) on the edges but the rest of the game decides it is too much for them and goes ballistic. The backrgound is missing, April herself leaves a trail that does not go away when you change a location.
I am gonna to tinker with Catalyst settings a bit and see if I can find a setup that will actually work. Hold on tight.
PS. I am on Radeon 4870 with Catalyst 9.8.

I have yet to try it, but i hope there is a solution. TLJ is nice the way it is, but having AA would be a great plus, especially since i'm on a 24"...

Coudl someone who has 4CD version check how FSSA works there?

I bought the Steam version a couple of years ago and still haven't played it due to the lack of FSAA. April is a walking pile of lego bricks and it drives me crazy.
Any chance that Funcom will update the GoG version to play nice with modern cards/drivers? As far as I know, this used to work on some GeForce cards with some versions of the game, but never with ATI...
If it was confirmed to work, I would just buy this again.

In my case I simply needed to restart the game. But from your post it sounds like you change the setting even before launching TLJ so I don't know.

I think it has something to do with
"[DirectX]
GfxDriver=display" <- this. I have no idea what options are available (other than "display") but I've also found out that changing GLOBAL settings for AA and AF works in TLJ like a charm.

Hmm, could you be a little bit more specific, please? Do you mean that I should make my changes in the "global parameters" instead of the "program parameters" in the nVidia control panel? If yes, won't it mess up with my other games on my computer, which are both very old and very recent ones? That'd be nice if i hadn't to mess up with the parameters each time I want to launch a game...
Could somebody post here the settings he/she uses in the nVidia control panl to run TLJ with AA please? (i'm on Win XP SP3)

No, in fact, i bought TLJ here, installed it, launched it to see what settings there were in-game. Then, I saw this thread on GOG forum and started to wonder if i could run TLJ with AA. I did the changes, then restarted TLJ, but to no avail...

Assigning a profile to game.exe doens't work for me either. I'm on a GTX 295 with 190.38 drivers.
Just force AA and other settings you want to use through the global settings, and after you're done with TLJ, restore them back to default.
About the settings:
I'm using 8X Antialiasing and 8X Anisotropic Filtering and the game looks great on a 24'' LCD. You can always try to play around with these settings...

Exactly.
It WILL mess everything up, unless you override the settings for EVERY OTHER game in the "program settings" tab. Sure - it's a bit of clicking to switch back and forth (or a while to set other games up in the second tab). I suggest you simply change it, play TLJ until you pass it and THEN change the setting back.
See below, for what it's worth...

I'm on a GTX 280 with the last nVidia drivers, which might be something along 190.60 or something like that. I'm also on a 24" LCD. Thanks for the advice (and thanks to Vestin too!) i'll try what you recommend.

Well, I saw that my "global parameters" are the default ones, so the "bit of clicking" should just be a matter of "click on restore", i think.
Anyway thanks a lot for your explanations and the pic enclosed in your post, that's very helpful ! And that's why i love GOG's players community so much ! ;) Kudos to you and Namur for the help !