Login to WordPress with email address.

login-to-wordpress-with-email-address.php

<?php

function login_with_email_address($username) {
    $user = get_user_by_email($username);
	if(!empty($user->user_login))
		$username = $user->user_login;
	return $username;
}
add_action('wp_authenticate','login_with_email_address');