Remove Widgets in Dashboard

I think the best way to go about this is to create a new plugin (or put in the theme function.php but a plugin will always work independent of theme) that disables the widgets you don’t need. Something like this.

function wpse_47707_disable_admin_meta() {
    remove_meta_box( 'dashboard_browser_nag', 'dashboard', 'normal' );
    remove_meta_box( 'dashboard_right_now', 'dashboard', 'normal' );
    remove_meta_box( 'dashboard_recent_comments', 'dashboard', 'normal' );

}

add_action( 'wp_dashboard_setup', 'wpse_47707_disable_admin_meta' );

See The Codex Page for more info on meta boxes