You do not have to provide an e-mail address, but if you forget your password, you will not be able to regain access to your account without one. In addition, you need to provide an email address if you wish to allow other users to email you from your User or User talk page using the Email this user feature. Your e-mail address is never displayed or given to anyone, with one exception: if you e-mail another user through Wikipedia, your e-mail address is included in the email, to enable them to reply.
You can provide an email address later on, or change it. If you change your e-mail address, you will need to reconfirm it. See Wikipedia:E-mailing users.
