Suppose I published a free chrome extension to Chrome Web Store.
Is it possible to get a list of e-mail addresses of people who downloaded it?
This is a valid question. I believe there may be good reasons for obtaining the email address of a chrome extension user for purposes other than SPAM. That being said, there is no way to automatically obtain a users's email. Suggested practices may include:
1) Directly asking the user to input their email.
2) Using the Facebook App flow to ask for permission to read the user's email address, which first notifies the user you are going to access this information.
It might be reasonable to first tell the user what you intend to use their email for (password recovery, notifications, etc).