Conversation Backup (1.4)
This tool can backup your SMS messages, MMS messages with included attachments, and call records, into a zip archive. You can specify a set of numbers to limit the conversations backed up. Optionally, you can request that those archived messages and/or call logs from your device are deleted.
This supports Android 4.0 and above.
Android Conversation Backup
This is a post for all my android users out there.
With Android, Google guarantees us that if we ever lose our android phones, we can just grab a new one. Once we sign in with our google account, it automatically syncs our emails, contacts, and applications (including the settings we have for those applications which support this).