How do I perform a full pre-rooting backup of an Android phone? The question arises because the best-rated backup application (Titanium Backup) requires root. So what would one use instead when getting a really complete backup is essential? Is there a file manager-type application available that enables copying the whole file system on the phone somewhere (to SD-card, online or wirelessly - doesn't matter which?)

(Samsung Galaxy S9000)
As far as I know, you can only make a full/complete backup of the phone with root.  Because you need root in order to run Titanium Backup (which only backs up apps and their data) or you need root in order to flash ClockWork Recovery which lets you perform a Nandroid backup (full image backup of the entire device).