fallout 1 works fine, but fallout 2 is no go... game start and after 5sec or 2 minuts whole system just stop responding (black screen)... not even ctrl+alt+del helps..
I tried updating , also unofficial patch and resolution patch and still no help...
Windows 7 x64 final (RTM) with newest Nvidia driver (8800GT GPU)

I assume you've tried the usual fix attempts, such as running as administrator, running in different compatibility modes?
You could try a virtual machine if you have a system able to run one at a reasonable performance.
However, once Windows 7 is released at retail, GOG should then be able to start patching to support Windows 7.

It works for me on 7 x64. Try running it in one of the compatibility modes and as an administrator.

I have same problem on same system here! Though I have an ATI Radeon 4870 1GB graphic card.
Fallout 1 - no problems,
Fallout 2 - black screen - ctrl alt del doesn't works. Computer is still running and if I try to remote desktop connection to "freezed" PC running gog.com's fallout 2 I could connect, but didn't get to the desktop. Only hard reset works.
This problem is occurring also running the game in Administrator mode.
The problem is solved with changing compatibility mode to Windows XP or Windows Vista.

For everyone who may still be having trouble with color problems or display problems with black screens, etc., check out this link. Randomnly found it in a topic on gamefaqs and it helped fix any display issues for me. If it doesn't work the first time then restart your computer and try again, it worked for me when the tool randomnly didn't work sometimes (probably just my computer). Hope this helps.
http://blog.macuyiko.com/2009/07/solving-color-problem-red-grass-purple.html