I've seen a hundred times when people was looking for a function that displays all the menu tree (including children) with all its parameters. This little function makes drop down menu available. The function that returns all the arrays of menu is:

menu_tree_all_data($menu_name);

Let's say you want to display all array of primary-links with it's children. Just write:

print_r(menu_tree_all_data('primary-links'));

Having this information is a good start to write a module that allows to display drop down menu.