Well, you could do an opt-out service -- send an e-mail that says "click here if this isn't you"

Or use something a simple screenname for authentication (e.g. the e-mail is just for lost passwords, so if they don't provide a valid e-mail, it's their loss).

Or use something like OpenID or Passport (the identity provider might need to validate an e-mail address but you don't have to).

Or build a site that needs no authentication to begin with -- e.g. a search engine.