SMS Backup+ is similar to CallTrack or SMS Backup, in that it backs up your SMS (and your call log) to the Google cloud, usually Gmail and Calendar. Youc an choose to backup only one or another.
SMS Backup will work with the new Google 2-step authenticator if you turn on plain-text authorization instead of the more complicated (but automatic) OAuth. You will need to create a per-app password.
The app runs in the background automatically, requires virtually no intervention.
If you want your stuff archived, this free solution is for you.
Rating: Get it