Call your VZW Voicemail (*86) and check and make sure you have it set to forward your voicemails to your device (this USED to be an option, so I apologize if the settings menu has changed, it's been a while since I have had to tweak with them).
I wouldn't say you HAVE to use Google Voice if you are satisfied with the default Voicemail service, however it wouldn't hurt to sign up for an invitation. I MAY actually have a few invites to give if you're interested. I use it myself, and it's a wonderful tool and app.