Automatically backup SMS, MMS and call log entries using a separate label in Gmail / Google Calendar. It is also possible to restore SMS and call log entries back to the phone (MMS not supported yet).
Remember to enable IMAP in Gmail and set the correct time/zone.
If you get a "You do not have permission to..." error or other problems during the first connect check the website for workarounds.
DROID X/2 users: due to a firmware bug (timezones) incoming messages might not be backed up. Complain to Motorola, don't blame this app!
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