Several Windows users have reported a mysterious file with the tilde symbol as it's name ( looks like ~ ) which recreates itself on the desktop frequently for what appears to be no reason.
MS hasn't confirmed this yet, but it has become somewhat apparent that this is in actuality a misplaced backup of your Outlook Express address book. The main addressbook should have an extension of .wab with your username as it's name.
One thing you can do to verify is do a Search in Windows for your username.wa like so...
On my system it would be a search (all files and folders) for bfarber.wa
Yes, I purposefully left off the b

The reason being is that there should also be the same filename, but with a .wa~ extension. This is the addressbook backup file. If you check it's properties and it's last updated timestamp is relatively old, this can help you to conclude it's not being updated properly.
The next thing you might want to do is for testing purposes, move the ~ file from your desktop to the same folder as your addressbook (found when you did the search), rename it "test.wab" and then doubleclick it. If it opens your addressbook succesfully, then you can confirm this is a misplaced backup indeed, and it can safely be deleted. Or better yet, rename this file from test.wab to username.wa~ and delete the existing copy of this file (you want the most current backup possible right

). Repeat this process whenever you see this file reappear, and bug MS to fix it.

Source:
http://www.pcmag.com