I noticed, on Safari, that the drop down did not function immediately, so perhaps there's a lag in the script being activated. Two versions of the jQuery library are being loaded - 1.3.2 locally and 1.4.3 from ajax.googleapis.com - which can cause problems.
^Both the above were Mac, so I'll comment as a Windows user, by saying it's working, and I checked the dropdown code and I don't even really see a reason why it wouldn't be working. Have you cleared your cache OP? Perhaps you're seeing an old version of the site.
I always have JS on. I never feel the need to turn it off.
When I find a JS-heavy site that people rave about, I like to see how it performs with JS off. Usually it's a disaster, but not always ... so I like to see what makes the difference. It's also a good test before deciding to use some off the shelf script (i.e. how does it perform without JS). I also like to test my own work with JS off if JS has been used to make sure it's usable without JS. And finally, when I'm debugging CSS for people here and their site is using a lot of JS, it can help to turn off JS so that Firebug is usable, as it often jumps all over the place if there is JS happening on the page.
Sometimes, though, I forget to turn JS back on again, and later I might be visiting a site like YouTube and wonder why everything is totally borked.