I know that I can put my phone next to my computer's mic and record messages that way but that is pretty low tech and fraught with problems. I'm a retired programmer, assembly language and C from before the days of Windows. It strikes me that it would be a simple matter to have a dialing program to dial the modem in my computer (yes, I still have one), access my voicemail and redirect the audio to a file. There would need to be an interface for delete, skip, etc... For those who don't have modems some sort of internet phone service could be used to connect to your voicemail account. Back in the day, this sort of thing would have taken but a couple of hours for me to cobble together a working model. Now? First, I'd have to learn all about programming under Windows. The point of all of this is, is there a program out there like what I propose? If not, how about one of you bright young guys writing one?
The easy thing to do is just sign up for YouMail (Visual Voicemail For Your Phone | YouMail) and copies of all of your messages will be emailed to you in *.mp3 format.