Can I force users to make unique e-mail addresses in django-registration?
It should suffice to create your registration form from your user model. If the e-mail address is defined to be unique there, the form will output an error on submit for duplicate addresses.
Look here for details.
As Dominic points out, you'll not be able to do this with the built-in user profile. You'll have to extend it by creating your own user profile as described here and make it contain a unique e-mail address.