I've just tried running the game (I'm actually running on Windows 7, inside a VM in OSX, but I'm 99% sure that's not the issue), and I'm seeing all the characters as weird garbled triangles, looking nothing like people. The 2D backgrounds display fine, and the game progresses as normal, but the characters are.. well.. like Escher paintings or something!

same here!
I guess it is the new nvidia driver.
a year ago, the game worked just fine on my winxp computer.

Same problem here, running on WinXP. One option is to regress to an older version of Nvidia's drivers but there is another workaround:

* Navigate to the %APPDATA%\The Longest Journey folder on your system - there should be a preferences.ini file there.
* Rename that file (e.g. to preferences.ini-orig) so you can go back to it if the following changes don't work.
* Use Notepad or other text editor to create a new preferences.ini with the following contents:

[Preferences]
SfxVolume=1.000000
VoiceVolume=1.000000
MusicVolume=1.000000
bool_Subtitles=1
bool_AprilHighRes=1
bool_ShadowsOn=1
bool_AllowFastForward=1
AudioDevice=autodetect
[DirectX]
bool_IsDoubleBuffer=0
bool_UseHardware=0
int_BitDepth=32
bool_ShadowsOn=1
bool_StartFullscreen=1
bool_ForceSingleBuffer=0

* At this point, if you run TLJ, it will most likely crash to desktop. To deal with that, navigate to the TLJ program folder (the default being Program Files\GOG Games\The Longest Journey) and find the game.exe file.
* Right-click on this, select Properties, click the Compatibility tab and tick the "Run in 640x480 screen resolution" box.
* Try running game.exe now and it should (hopefully) work with the 3D models now fully visible.

What this workaround does is run TLJ in software mode, with the 640x480 switch needed to run it fullscreen. The only visible difference with software mode is that shadows are now dithered, but for most that should be a small price to be able to replay an old favourite.

@ astralwanderer: cool it works! you are my HERO !!! :-)

Thanks for the confirmation Falke81 - is this on WinXP or a later version?

I use winXP !
finally I am able to play again.