Problem: we want the styles of, say, the titles or the backgrounds to depend on the chosen menu item.

Solution: in Joomla 2.5 it's as simple as :

<div class="menuid_<?php echo (JRequest::getInt( 'Itemid', 1, 'get' )); ?>"

Then in the css file we just style .menuid_X and its children (X being the id of the menu item).