I've been wondering this too...

 

Sprint and AT&T (and probably others) have an option in the voicemail system to not ask for a PIN if you're calling from your own phone. Verizon doesn't seem to have that.

One "solution" is to use Google Voice and busy/no-answer forwarding -- not only does it have the option to not ask for a PIN from your own phone, but it can transcript and SMS you the message itself (not perfectly, but well enough to get the gist of the VM and decided whether it's important etc).

 

YouMail also has this feature (not requiring your password if calling from your own phone). However, don't use the actual YouMail app as it eats battery life -- call into each each time.

 

Alternately you can set up the VM speed dial to also send your password. While that will keep folks from KNOWING your password, it will also make it easy for anyone who access to your phone to call in to your voicemail.

If you want to do this, the setting for it is under settings/call settings/voicemail.
On mine I have two pauses (the 'P' on the setup screen) before it dials my password. Be sure and put a '#' (pound sign) after your password because the VM expects that.