Didn't test it, but probably the spot do to this would be in /scripts/adduser.inc.php
// Make sure Email and Email_verify are the same
if ($Email != $Email_verify) {
$html->not_right($ubbt_lang['EMAIL_NO_MATCH']);
}
// ------------------------------------------------------------
// If all required info is not filled in, then we can't proceed
if((!$Loginname)||(!$Displayname)||(!$Email)||(!$Email_verify)||(!$Password)||(!$Verify)){
$html -> not_right($ubbt_lang['ALL_FIELDS']);
}
There's the code that requires the e-mail addresses. So you'd have to remove the check there, and remove the e-mail stuff from the registration screen template and profile.
If the e-mail address is optional, you could just remove the check, and remove the e-mail verification stuff.