I don't think you can do this without being jailbroken. If you are, then search for Voicemail Forwarder in cydia.
On a side note, Just to let ya know about an alternative voicemail experience.
I use an app from the App Store called YouMail. You have to make an account, but it's free and awesome, and very very customizable. With YouMail, you can email them to yourself and even post your voicemails on any website, like Facebook, and twitter, etc.
You also receive a push notification instantly after someone leaves a voicemail just like the real Phone.app does (I have tested this many times to make sure it does). You can choose custom greeting for certain contacts.
I have mine setup so whenever a blocked number calls me, it goes straight to a message saying my phone does not except blocked calls.
Whenever I get a call from a number that is normally not blocked, but the person blocked it before calling me, it brings them to a message that say "Sorry, this number does not except blocked calls. Please unblock your number and try again". I know that is not what you were asking, but I thought I should let you know a few other reason why I think it's worth it to take the time to setup YouMail.
Also, You know how you cannot get visual voicemail unless you are using your carriers data connection? With YouMail, you always have visual voicemail whether you are connected to data or WiFi.
And if you don't care about VVM, then just dial your phone number, and you can listen to your voicemail that way. I save my own phone number in my contacts as "Voicemail".