Are you using Visual Voice Mail or standard voicemail? What Droid and what version of the Android OS are you using?
Standard voicemail - you do dial *86 or your own phone number to access, then enter your password.
With the free Visual Voicemail (Android 4.4 +) you will see the VVM icon, and when you tap that, you can play your messages with no need to enter *86 or your password.
Premium Visual Voicemail is a an extra monthly charge; if this is the prompt you are getting for a free trial you can decline and ask not to see it again.
If none of this addresses your problem, please provide more information so we can answer more accurately.
I'm still confused over what voice mail service you have, and what you want to get rid of.
You can always log on to your verizonwireless.com account, and go to the voicemail options, to check what you are currently signed up for and change it if it is not what you want.
BASIC voicemail - included in all plans, works on all phones, dial *86 and enter a password to access.
Visual Voicemail - $2.99/month, for non-smartphones and some older smartphones
BASIC Visual Voicemail - included for newer smartphones
PREMIUM Visual Voicemail - $2.99/month, more features and options than the BASIC
I have voice mail. And it works just fine.
It's just that when i get a VM and slide/swipe the notification screen down to retrieve it. I get this prompt; "Please accept the Terms and Conditions if you would like to hear voice mail via Visual Voice Mail." That's what i'd like to stop seeing. So far i've checked in settings and notifications and haven't found way to stop receiving that prompt.
And underneath that prompt i also get *86. The first time i received that prompt, i believed that by swiping it, it would stop it reoccurring. It hasn't. Also when i swipe it, the *86 goes with it. So then i have to manually dial *86.
P.S. I just checked my phone and i have a VM. This time i know better. I'll just press the *86.
Or you can try the visual voicemail - you listen to your messages just like regular voicemail, but you don't need to dial *86, and you can save them as a sound file on your phone forever if you want. Once you get the visual voicemail, that prompt will go away. You can go into your account and go back to basic or give the vvm a try.