Anonymous users cannot register for a civievent
When you create an Event you specify what Profiles should show eg at http://d46.demo.civicrm.org/civicrm/event/manage/registration?reset=1&amp;action=update&amp;id=3 you can see it has Include Profile = Your Registration Info.

In this case it sounds like you have some other Profiles in use (instead or as well)

And either those Profiles are "not configured to be used for 'Profile' listings in its Settings" - which is what your error says - or the Profile might have incompatible fields included in it.