Retrieve the e-mail address of a Google Form respondent without asking for their e-mail address in the form

This can only be done if you are using Google Apps for Business, Google Apps for Education, or Google Apps for Your Domain, and are having users on your domain fill out the form. In that case, you can use getRespondentEmail() to retrieve the submitter's email address.

If your situation doesn't meet the requirement above, Google does not expose the submitter's email address to you and your only option is to prompt them for it on the form.