Not deleting the file bncache.dat - from your StarCraft Folder after having a crash from Battle.net that returns you to your desktop. If you ever crash off of Battle.net, you need to delete the file bncache.dat. Whatever you try after that to fix the problem could be masked by the fact you have a corrupt bncache.dat file. A corrupt bncache.dat file can crash you even if you fix your problem by something you did to correct it.
Running extra programs - in the background, especially MS Office Toolbar, MS Fast Find and ICQ. Virus Scanners can cause it also (although it is rare). I have noticed the Windows NT systems will have crashes more often when ICQ is running also. Before you get on the internet, and before you play Starcraft, you need to delete the file bncache.dat from your StarCraft Folder if you are trying to fix a crash. You then need to hit ctrl+alt+del and end task on all programs except for Explorer, Systray and Point32 if you have it. Then you connect to the internet, if ICQ comes up, end it, you should disable net detect. Then minimize the connection window, if your browser automatically comes up when you connect to the internet, close it, you do not need it open. Then start StarCraft, and get on Battle.net.
Mismatched Ram - if you have recently added any Ram memory to your computer and you are not sure if you added the same speed Ram, your computer will definitely crash when trying to play StarCraft. If you have experienced a crash and you recently upgraded your memory, here is what you can do. Pull out the new memory, if you still have 16 meg without it. Delete the file bncache.dat from your StarCraft Folder, and try again. If you are able to play, then you know its your Ram that is causing it.
I do not feel that this is all of the reasons for that crash, these are just the ones that I have been able to verify. If you have previously tried something before, and it did not work, and you did not delete the file bncache.dat from your StarCraft folder before you tried it, try it again, but this time delete that file.
Source:
Starcraft Support
Covers most of the Access Violation Errors listed there.