Something similar is called xArchive. It automatically backs up any SMS, MMS, Photos, and videos into Gmail. It is one of those apps you install in the background and forget it. Every so often when my SMS counts get high, I check Gmail just to make sure they are all accounted for, then delete them from my phone.
I am shocked Google doesn't offer this option natively. They already archive your IM's through Google Talk - it seems like a natural extension...