This is a fork of the Android backup tool SMS Backup, where development has stopped a while ago. It uses Gmail to perform SMS, MMS and call log backups over the network.
Main differences / improvements:
New restore feature. SMS stored on Gmail can be transferred back to the phone. This even works for users who have already created their backups with older versions of SMS Backup. Note: MMS are currently not restored. More Info »
XOAuth: SMS Backup+ will never ask you for your Gmail password. Instead it uses XOAuth to get access to your data. You can revoke the access rights at any time.
MMS backup support (since 1.1), only available on Android 2.x
Call log backup (since 1.2), with Google Calendar integration (since 1.3.)
Faster backups. SMS Backup+ saves around 30% of data transferred by avoiding Base64 encoding of emails.
Batch size limits removed.
Works with any IMAP server (but defaults to Gmail).
Tested with Android 1.5 - 2.2.
SMS Backup+ is available for free in the market, there will never be a pro / paid version.