Most web based community systems use your e-mail address to have at least some form of verification who you are, or to contact you with solicited (and unsolicited) information.

But what to do when a new user signs up and doesn't even receive the initial account e-mail because the address was entered wrong in the sign-up sheet? How is that user ever going to reset his/her password or gain access to the web-site?

A new authentication system is needed, one that does not simply rely on a username and a password. This is Ali Baba in perpetuity.