Better than that, Gmail does this automatically. Login to Gmail on the computer after your phone has synced up, and all your contacts are there. Correct information, merge duplicates, etc. Say something happens with your phone, you can factory reset (where you lose everything), just login to Gmail when you set it up, and all your contacts come right back. You don't need to do anything and you definitely don't need an app.
My Contacts Backup is not worthless, though. If you're planning to switch to a BlackBerry or Windows Phone, run it and have it make a backup. Then re-sync on the new platform. But if you plan on sticking with Android, there's no reason to want to keep it.