I don’t know the exact definition of a drop-down menu, but with a free plugin called jQuery Categories List Widget you should get a tree view with your top categories as expandable/collabsible branches. Kinda.
I use it on kvarnexperten.se/wp (under “Innehåll” on the right), but I have tweaked the code so that it does not collapse but always displays all items.
I found this thread searching for ways to include post images in category view, thanks for putting me on track!
