SMS Backup+ - Backup Android SMS, MMS and call log to Gmail / Gcal / IMAP - jberkel/sms-backup-plus
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 & Restore - Simple Android app that backs up and restores your phone's text messages, and call logs too
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.
Super Backup & Restore - Super Backup & Restore app allows users to backup all their stuff such as pictures, videos, apps, text messages, contacts, call history, and calendar data, etc.
My Contacts by Captain Tushar - My Contacts is an app by Captain Tushar that comes up with features to help you in managing your contacts list so you can effortlessly delete or edit existing contacts.