There is no simple way for users to change their login password
In GNOME 2, a user could change their password by choosing the 'About Me' option from the Indicator Session menu.
With Unity in Natty/Oneiric/
It is proposed that a more obvious way to change your password be introduced, ideally by typing the word "password" into the Dash and clicking on an icon titled "Change Password", which would open up a dialog window similar to GNOME 2's About Me application, but with a focus on changing your password. A menu entry titled "Change Password" could also be added to the session indicator menu.
In addition, changing your password in this manner would also update your GNOME Keyring encryption password to match your login password.