Wide Angle Contact Transfer - Contact Transfer- easily manage contacts between iPhone, Android & PC with this Windows software. Transfer contacts directly between devices and edit them from your PC!
SMS Backup+ - Backup Android SMS, MMS and call log to Gmail / Gcal / IMAP - jberkel/sms-backup-plus
Epistolaire - Open source SMS and MMS backup app. Can convert to HTML, XML, Maildir (for emails).
oandbackup - Make backups of selected apps on your device and restore from those backups.
SMS Backup & Restore - Simple Android app that backs up and restores your phone's text messages, and call logs too
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.