If you are using Visual Voicemail, or a third party service like You Mail or Google Voicemail, then you can check the trash bin and see if it may still be there.
Using Verizon's standard voicemail, there is an option while you are in the voicemail to listen to recently deleted messages, and you can restore from there. If you have deleted a message and then left the voicemail system, I don't think there is a way to recover deleted messages.
