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+ - Backup Android SMS, MMS and call log to Gmail / Gcal / IMAP - jberkel/sms-backup-plus
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.
SMS Backup & Restore - Simple Android app that backs up and restores your phone's text messages, and call logs too
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.
Epistolaire - Open source SMS and MMS backup app. Can convert to HTML, XML, Maildir (for emails).