Get the free 'file' command:
http://gnuwin32.sourceforge.net/packages/file.htm

For Windows XP go to: \Documents and Settings\(username)\Application Data\Apple Computer\MobileSync\Backup\

For Windows Vista and Windows 7 I've heard it is this, but have not confirmed:
\Users\(username)\AppData\Roaming\Apple Computer\MobileSync\Backup\

The voicemails (I did this on XP) are in files with no extension. The file command can figure out which files are audio files and the following command line (you will need to modify it to include it in a batch file) uses the file command to copy off the audio files (they are all voicemails it seems) to .amr files which can be read by QuickTime or maybe the Real Player:
@for %f in (*.) do @(for /F "usebackq tokens=1,2* delims=; " %g in (`file %f`) do @(if %h==Adaptive copy %g %g.amr))

I also learned from this post, so credit due:
http://www.instructables.com/id/How-to-Download-Voicemail-from-an-iPhone/

pushd ~/Library/Application\ Support/MobileSync/Backup ; for I in `find . -name "*" -exec grep -la '#\!AMR' {} \;` ; do cp $I $OLDPWD/$I.amr; done ; popd

If you're on Windows, you might be stuck with the much more expensive The Missing Sync. In either case, I'd say one of those two is going to be your best bet – hopefully you have a backup that was made recently enough to have the voicemails. I would probably avoid creating any new backups for the time being just in case a newer backup might overwrite an older one.

I am desperate for your assistance. Somehow AT&T wiped out all of my saved voicemails during an upgrade on my iPhone 4 from the original OS (4.0) to the current OS (4.2.1). The voicemails wiped out were only saved ones (about 20 or so), new, unlistened to messages (2 from October), were retained and accessible. I contacted AT&T and after a couple hours between different departments, i was told my messages are gone!

My hope is that I can retrieve the messages from a backup file. The reason for the dire need of the files is that I have messages from my mother (she unexpectantly passed away in October) to my kids, singing happy birthday and other fond memories.

If you have any suggestions I would be highly appreciative and grateful for your efforts. Thank you!

The script was just for OS X users, though it sounds like you must have Cygwin installed to be getting as far as getting an error from bash. I don't have a Windows 7 machine to try something similar on, with or without Cygwin… and according to Fred above, there are no more .mddata files with iOS 4.x. Soon as I get an iPhone 4 (hopefully on Verizon), I'll update the script.

This script does not work for me. I get an error saying

bash: pushd: /home/Raj.More/Library/Application Support/MobileSync/Backup: No such file or directory
bash: popd: directory stack empty