SMS Backup+ - Backup Android SMS, MMS and call log to Gmail / Gcal / IMAP - jberkel/sms-backup-plus
oandbackup - Make backups of selected apps on your device and restore from those backups.
SMS Backup Android - SMS Backup Android is a free Android application which allows users to backup and restore SMS...
SMS Forward - SMS Forward is a simple app that allows you to redirect SMS you receive on your phone to another device.
Titanium Backup - Titanium Backup is a very old backup app that has been around since the early days of Android. In fact, it's one of the few apps that covers all versions from 1. Read more about Titanium Backup.
SMS Backup & Restore - Simple Android app that backs up and restores your phone's text messages, and call logs too