How to register for event without an email address?
Make email address field not-required on the profile you include on your event online registration form.

If the registering participant does not provide an email address, you could get duplicates in your CiviCRM contacts. See this warning:


  Duplicate Matching Impossible The selected profiles do not contain the
  fields necessary to match registrations with existing contacts. This
  means all anonymous registrations will result in a new contact.