Sudden PC shutdown also occurred when having videos on Skype (incoming and outgoing). So I think the problem may not be with Avast!, or at least with its compatibility with other softs such as skype, windos live messenger, µtorrent, etc .
No incompatibility as far I know.
Are you sure your computer is clean, without virus?
Also, check the folder <avast>\data\log
Are there any files called unpXXXX there (where XXXX is a random number)?
If so, send them to vlk (at) avast.com
They may contain more information about the problem (maybe a link to this thread).
Are you using Windows XP?
If so, please, go to folder \windows\minidump and send the newest (recent) .mdmp files for analysis.
Better if you can compress (zip) them and add some information about the BSOD and the link for this thread.
Send an email to any of these addresses:
vlk (at) avast.com
rypacek (at) asw.cz
Or upload to the any of these anonymous ftp servers:
ftp://ftp.asw.cz/incomingftp://www2.asw.cz/incoming