So that users don't have to remember a username, my webapp doesn't ask users to enter one (accounts are private and there are no profiles or user-generated content). However, I would also prefer not to send users a confirmation email when they sign up, since I don't use their email addresses to send them things (except when they reset their password).
However, I recognise this could lead to problems if someone signs up with the wrong email and then the person that really owns wants to register. What is the best way to handle this?