For a typical land line service, you can keep your number if you are moving within the area served by the same central office. To know for sure, you need to ask Verizon.
Another option is to port your number to a VoIP provider before you move. Then, you can use it anywhere that has interenet. However, you won't be able to port it back to traditional phone company unless you happen to live in the area the phone number first came from.
Some options for VoIP service include Google Voice, Vonage, ooma, and Nettalk. There are plenty of other options, too.