iPhone FTP utility with automatic backup?
What you want can be done with Apple's iCloud backup (on your iPhone go to: Settings, iCloud, Storage &amp; Backup, iCloud Backup). But you ask specifically for a whole iPhone backup over FTP.

You can also use your WiFi to backup your iPhone via iTunes. To set up Wi-Fi syncing, connect your iOS device to your computer with the included USB cable. Click the Device button in the upper-right corner. (If viewing the iTunes Store, click the Library button first.) If you don't see your device, choose View > Hide Sidebar. In the Summary tab, select "Sync with this [device] over Wi-Fi."

There are some good non Apple programs to backup your photo's over the internet (bittorrent sync, Dropbox, Copy for iOS, and much more), but none use old school FTP.

If you specifically want FTP, you should jailbreak your iPhone, setup your FTP connection and run a Cron job which syncs every x hours. I would strongly recommend not to go this way, it will eat your battery and FTP is not the correct way to do this, I would greatly suggest rsync over SSH. Or use SFTP. But yet again, I would strongly recommend not to go this way.

If you want to drop every photo you make onto an FTP host, you can do this if you setup an OS X device in between. You can use iCloud-Photostream to send the photo's to your photostream. Now, when your mac is running, it will automatically download this stream and store the foto's in ~/Library/Application Support/iLifeAssetManagement/assets/sub. Now you can use any software to start syncing your mac. For example you can create 'Folder actions' to start an FTP upload every time the folder gets a new image.

Another possibility is to make the photo from within file-exchange app like Dropbox or bittorrent sync or one of the others. The app will automatically upload your photo's to other devices.

I would go for the iCloud-Photostream -> Mac -> Client if I had to use it myself. I would go for creating the photo's from within the file-exchange app if I had to explain my mother how to do it. Furthermore, what are you planning to do with your backups? You can not use them to restore your iPhone, you need an iTunes or iCloud backup for that.