Simply paste the following into your functions.php file. The code will remove all dashboard widgets, so you should comment lines related to wigets you'd like to keep.
function remove_dashboard_widgets() {
global $wp_meta_boxes;
unset($wp_meta_boxes['dashboard']['side']['core']['dashboard_quick_press']);
unset($wp_meta_boxes['dashboard']['normal']['core']['dashboard_incoming_links']);
unset($wp_meta_boxes['dashboard']['normal']['core']['dashboard_right_now']);
unset($wp_meta_boxes['dashboard']['normal']['core']['dashboard_plugins']);
unset($wp_meta_boxes['dashboard']['normal']['core']['dashboard_recent_drafts']);
unset($wp_meta_boxes['dashboard']['normal']['core']['dashboard_recent_comments']);
unset($wp_meta_boxes['dashboard']['side']['core']['dashboard_primary']);
unset($wp_meta_boxes['dashboard']['side']['core']['dashboard_secondary']);
}
if (!current_user_can('manage_options')) {
add_action('wp_dashboard_setup', 'remove_dashboard_widgets' );
}