Upon trying to play The Longest Journey downloaded from GOG.com the intro video isn't shown (I can only hear the sound) and the 3D models during the first scene seem to flicker.
I have an NVIDIA graphics card with the latest drivers.
After some searching (too much, that's why I'm posting the answer here) I found a solution on the forum of Good Old Games.
Adding the following DirectX section to "preferences.ini" file located in "C:\Users\UserName\AppData\Roaming\The Longest Journey" seems to solve the issue:
[DirectX] GfxDriver=display int_BitDepth=32 bool_IsDoubleBuffer=0 bool_UseHardware=0 bool_StartFullscreen=1 bool_ForceSingleBuffer=1
I had problems that the videos are not shown under Windows 7.
Setting the power management profile to high as suggested on http://forums.steampowered.com/forums/showpost.php?s=e3142ace9a721eae18133bc593808ddd&p=23595047&postcount=9 solved the problem for me.