Try setting up a new contact for Voice Mail that looks like this: *86,,****
where the asterisks represent your password. The commas are for pauses. Then whenever you dial that contact, it will call Voice Mail, wait for the Voice Mail Lady to ask for your password, input your password, and take you to your messages.
You can't get rid of the password for Verizon voicemail. Tikibar has given you a way to automatically put it in so you don't have to do that everytime.
You can also use a third party voicemail service like YouMail that does not use a password to retrieve messages.