Generally, files beginning with a ~ are temporary backup files created by
programs like Word, Excel, etc. You might notice that if you keep your files
in a directory, and you are working on a file such as thisfile.doc, you'll
see something like ~hisfile.doc slightly greyed out in the same directory.
If your computer was to crash while working on the file, you should be able
to re-open Word or whatever program crashed and you will be prompted for
recovery. These files are normally deleted once the program closes without
an error, but sometimes they stick around.
It's likley that ~*.doc is safe to delete (same with ~*.xls, ~*.ppt etc),
but I'd do a search for them first, and give a quick check on the remainder
of the file name and location before deleteing. If it looks like a document
you've worked on, it's probably fine, if it's in the windows system folder,
maybe not.
Remember though, delete at your own risk!
-Will