Ubuntu and probably a lot of other distributions do not allow you to set a root password. Instead they encourage users to use sudo.
This irritates me greatly, and the way to set a known password for root is to use sudo itself, together with passwd:
~$ sudo passwd [sudo] password for martin: <I type my own password> Enter new UNIX password: <I type root's new password> Retype new UNIX password: <I re-type root's new password> passwd: password updated successfully
This updates root's password and needless to say you should use a long and complex string of characters.
If you need a password suggestion: Think of a line from your favorite poem (or song!) and use the initial letters from each word, including capital letters and punctuation. Your new password must be at least ten apparently random letters for it to be secure.
You're unlikely to be successful when using a correctly set up multi-user machine, where a normal user will not be a member of the sudoer's elite - those permitted to use sudo.
