Limit username to specific characters (A-Z and 0-9)

Using the regex posted by Moaz (and adding capitals), we will need to hook into the registration_errors filter:

// Restrict username registration to alphanumerics
add_filter('registration_errors', 'limit_username_alphanumerics', 10, 3);
function limit_username_alphanumerics ($errors, $name) {

 if ( ! preg_match('/^[A-Za-z0-9]{3,16}$/', $name) ){
    $errors->add( 'user_name', __('<strong>ERROR</strong>: Username can only contain alphanumerics (A-Z 0-9)','CCooper') );
 }
 return $errors;
}