SMS Backup+ - Backup Android SMS, MMS and call log to Gmail / Gcal / IMAP - jberkel/sms-backup-plus
Wondershare MobileTrans - Wondershare MobileTrans is a 1-Click Phone to Phone Transfer for you to move data between devices with different operating systems. Your must-have phone Transfer.
SMS Backup & Restore - Simple Android app that backs up and restores your phone's text messages, and call logs too
SynciOS Data Transfer - SynciOS Data Transfer is a mobile app that acts as a third-party alternative to the standard syncing app on the Mac system, which is iTunes.
Epistolaire - Open source SMS and MMS backup app. Can convert to HTML, XML, Maildir (for emails).
SyncDroid - SyncDroid is basically and iOS and Android smartphone manager that lets the users of both smartphones to transfer their mobile content from one smartphone to another within few simple steps.