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Question: How do I get my voicemails off my iphone onto my computer?

Answer: There are two ways to go about this, the file transfer way and the manual record way.

The File Transfer Way
This will require your phone to be jailbroken.

Don’t know what Jailbreaking is? Read here http://en.wikipedia.org/wiki/Jailbreak_%28iPhone_OS%29I use the iphone browser tool from Google to look through all the nooks and crannies of my iphone
http://code.google.com/p/iphonebrowser/downloads/list

Once you’re connected to the device using the iphone browser tool, browse to /private/var/mobile/Library/Voicemail/ to view the list of VM files.

From here you can right click the file and save it to your computer.

They’re saved as .AMR files, which QuickTime can play.

The Manual Record Way

If you’re iPhone is not jailbroken (or not even an iPhone at all), you can also utilize your phone’s headphone jack and your computer’s line in.

Connect the phone to the computer using an audio line, usually a 1/8 male to male easily picked up at Radio Shack, and fire up your favorite recording software.
Play the voicemail and record the result with your favorite recording software.
Note, however, that not all phones have standard headphone jacks out—the first generation iPhone has the recessed jack, and other phones often use non-standard headset jacks, too.

As for recording software, the standard windows recorder will not quite work for long messages.

I think it is limited to one minute.

Some great Audio programs to use would be Audacity, or VLC player.
http://audacity.sourceforge.net/
http://www.videolan.org/vlc/