Verizon Wireless only keeps a few days worth of text message content on their servers. A court order is required to retrieve them. The text message log (numbers and times) are available for 90 days worth on your MyVerizon account online. You can download that information to an Excel spreadsheet.

The Android devices do also have the option of a third party application from the Play Store to backup and even restore your text messages from one phone to the next. You can also email the backup file to your email address if desired. You do have to have the application installed and running in the background before the messages are deleted from the device. I personally use SMS Backup and Restore which saves the backup file to the SD/storage of the phone as an XML file. I can then email that file to myself and print it out with my computer.