oandbackup - Make backups of selected apps on your device and restore from those backups.
Save contacts - Save contacts app provides features through which users can select the desired data to create the backup in a variety of different formats.
SMS Backup+ - Backup Android SMS, MMS and call log to Gmail / Gcal / IMAP - jberkel/sms-backup-plus
G Cloud Backup - The easiest Android Backup app that protects all your contacts, call logs messages, music, videos, family photos, and other personal (irreplaceable) data to secure, cloud-based servers for Free
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.
X-Transfer - X-Transfer is an app by WebToGo that comes up with features to help you in performing data transfer between your smart devices in a few simple steps.