sudo tar czf /backup.tar.gz \
--exclude=/backup.tar.gz \
--exclude=/dev \
--exclude=/mnt \
--exclude=/proc \
--exclude=/sys \
--exclude=/tmp \
--exclude=/media \
--exclude=/lost+found \
/
Add more --exclude= parameters if you need to.
It will create an archive of all your files at /backup.tar.gz, which should be copied to another computer or drive.
To restore your files when the system goes pear-shaped, use a Live CD. Mount the bad system under /media or /mnt and then run tar xf /path/to/drive/with/backup.tar.gz -C /mnt (or /media).