After trying several things (changing compatibility mode, Quicktime settings), it seems I find Myst crashing during video or animation sequences in the game. Without the videos (e.g. running it in Windows 2000-mode), the game functions without crash, however, certain puzzles cannot be interacted with appropriately without videos, and well, yeah, I'd like the animation, because that is part of the game.
And since I cannot really find anyone with a solution specific to videos causing crashing, I decided to start a new thread and ask. I have also sent this issue to GOG.com themselves, but I may be slightly impatient. Or perhaps, I just wanted a solution in case others had the same issue out in the open.
Oh yeah, I run Windows 7 64-bit which might help get on the specifics.

The combination of compatibility settings that work for me are, Run as Admin, XP compatibility and Disable Visual Themes. I'm also on Win7 64.
Hope that helps.

Hm, I have the same settings, which still causes problems. What are your Quicktime settings? And more importantly, which version of Quicktime do you use? I use Quicktime Lite, but I may need to try the Alternative version.
Edit: Hm, not so lucky, I'm afraid. QuickTime Alternative and QuickTime Lite seems rather similar. I tried turning off all the extra settings for video, but still kept DirectX on (safe mode haven't helped), but the result is the same. Eventually, during an animation (but it can actually go through a couple of animations just fine) it gets stuck and needs to be closed via the task manager.

My QT version shows 7.6.6 (1671) and it got installed along wtih iTunes. I haven't changed any of QT's settings, so i guess it's using the deafult settings. I checked the Advanced Video options and DirectX is on, with all 3 checkboxes ticked.

Well, I am at loss. Nothing I do makes this game function. Maybe there is another trick to it, but I just haven't found it yet. Or maybe I just have to give in and try to make it run in Wine on Linux instead.

Do you have XP mode installed on your Win 7 ? Maybe it's worth a shot.

I'm having the same issue. I can usually get through a few video shots, but eventually, the game game freezes up and I have to kill the process.
Running Myst ME on...
Windows 7 x64
--XP Compatability Mode SP3
--Desktop Themes Disabled
--Run as Administrator
Quicktime 7.6.6
Pentium Quad Core
Nvidia 9800 GTX+
I did try changing the process affinity to only one core, but that did nothing noticeable.
I believe the lock-up is a Quicktime problem, but I have yet to find a solution. Other versions of Myst are fixed by changing the FIFO rate in Quicktime to 200, but there doesn't seem to be any such option in Quicktime 7.6.6.
If anyone figures out how to make this work, please post what you did.
-Khalaq

I'm having the same issue. Its a tad more stable in Win 98 compatibility, but thats it. Not a whole lot of difference. Also, the animation and sound is choppy.
EDIT: Beat the game! Managed to solve video issues with XP running on a VM (Virtual machine). Not the best solution, but it works.