Ubuntu uses sudo in its privilege elevation model, so essentially your password is used as the root password because you are in the sudoers file.
As for it not prompting you to enter it every time you "sudo" there is a period of time where it will remember the elevated authentication. Now, if this is happening all the time without you ever having to type in a password it could be(most likely) that you are somehow in a group that allows running commands as root without authentication, the wheel group etc. This can be checked by looking into /etc/group and running visudo from the # terminal and looking for your username or group in that file.
Now to change the root password in Ubuntu you need to open a terminal, type
sudo -s, then
su root, this will switch you over to the actual root user and from here you can then run
passwd and set a root password.
Here is the process for changing passwords as the root users for others.
[dan@Archimedes ~]$ su root
[root@Archimedes dan]# passwd dan
Changing password for user dan.
Retype new password:
passwd: all authentication tokens updated successfully.