I wouldn't necessarily recommend doing this because it seems inefficient and I think there could possibly be some issues trying to copy stuff from /proc and there are a lot of symbolic links in some of the sub directories in /lib and you would essentially double the space used in the root partition so you need to make sure you even have room before you try to copy everything, but if you had to:
Code:
ls -a / | grep -v root | xargs -i cp -r /{} /root/backups
ls -a /root | grep -v backups | xargs -i cp -r /root/{} /root/backups
you would basically be taking all the root directories, excluding /root and then copying over into root/backups. Then since you did not copy /root into /root/backups you would run the second command to copy everything from /root except for the backups directory into /root/backups.
I think elija's option for rsync might be better, but I am not as familiar with how rsyc works as I wold like.