Well, this depends.
Are you using an Android, Blackberry, IPhone, FirePhone, or any other kind?
For Android and IPhone, I know for a fact there is an app to do this.
For old flipphones, and the newer androids and iphones, you can also copy the messages over to your sd card.
Blackberry, I don't have much experience with, and the same with Firephone, but I imagine it would be the same.