Examples migrated from Codex.

Note: The examples below should be called immediately upon plugin load or placed in theme’s functions.php file.

This code would turn the display status of the Toolbar to off.

add_filter( 'show_admin_bar', '__return_false' );

Alternatively, you could write it into a full fledged function.

add_filter( 'show_admin_bar' , 'my_function_admin_bar');
function my_function_admin_bar() {
	return false;
}

This would hide the Toolbar for all users except Administrators.

add_filter( 'show_admin_bar' , 'my_function_admin_bar');
function my_function_admin_bar($show_admin_bar) {
	return ( current_user_can( 'administrator' ) ) ? $show_admin_bar : false;
}