I know, to some this may sound like more trouble than it's worth. But I wold like to know what files/folders need to be copied, so that if the system were to be installed on a totally different computer but with all the same users - the look, feel, bookmarks, browser preference settings, exc. will be identical to the way it was when the backup was made, without the need for the user to set them (just copy the data back, if need be alter a file or two, but nothing that individual users would need to do, just whoever put the system there.).
If possible, even keep the same password for each user, even if you don't know what it is (but I know that may be pushing it too far, and it's not all that important - but look, feel, exc. is the main thing I am after.).

It's pretty easy to clone a system (basically cp -a /* /new/partition/), but as for recreating all the user accounts and settings on a different system that's already been installed, it could get very messy.

Unfortunately, I figured that. But messy or not, the data has got to be there somewhere. But so far all I have managed to backup and restore in this manner is the Firefox bookmarks. Some other files I THOUGHT I had figured out what to do with, but the restore process only caused that user account to "jam" during sign in.
I know this will most likely NOT be the last "messy" thing I try to do with Linux either. Just the way I am, I have always gotten down to the "nitty gritty" of data backup/restore in any OS I was using at the time. (Even when I still HAD Windoze installed, I was able [after some time figuring out what was what, data wise] literally backup everything so that restoring the entire OS to a different machine completely had no difference from when the data was backed up, as far as look, feel, user accounts, exc. goes - this included everything, EVEN the PW of accounts when it was unknown to me [but of course Administrator access was requires] and the "registration" info for a lot of commercial software - even what to alter if the new system had things in different locations. That is what I am trying to get to with Linux right now).

I have done this many times. It really is a lot of work.

I would suggest you make a backup of home and root with hidden files, including the desktop for kde. If running mysql you will have to to a mysqldump to the home directory as well.

Other files are important such as etc/hosts and etc/sysconfig/network.
Apache config files as well, use webmin to find their location. You may also have added items to rclocal in etc/rc.d

You will also have to copy the mail spool etc if you are running sendmail and postfix.

I am sure there is more but making sure you copy the hidden files.

My first reaction to your question is to create an image of each partition on your system. As far as I know, the best way to to image a partition is from a Live! CD. In Linux, the most popular tool is partimage. I use System Rescue CD here because it includes Partimage, Gparted and several other utilities that may be useful when the worst happens. Partimage copies only the used portions of your partitions and the images can be compressed to reduce size. I do not know if this will work for you, but I hope it helps.