As seen here:
http://www.vbulletin.com/forum/forumdisplay.php?1
(The Forum Tools - Search Forum part)
I help run a major phpBB forum and would like to incorporate a menu with identical functionality.
I assume there are existing scripts/widgets that do this. I’d just like some guidance in selecting an elegant solution.
Thanks! 
It looks as though they are using a YahooUI library to implement the menu functionality (presuming you are refering to the menu with ‘Community’, ‘Forum Actions’, ‘Quick Links’ etc.)…
You can either rip it from there JS files (see the PopupMenu function/s in the vbulletin-core.js?v=403c file…make sure you check there license terms) or you could pretty easily mock one up if you were to use jquery or some other framework.
Good luck