I like drop down menus, but they have to be done correctly. It is a shame to miss out on good mobile traffic because the drop down either doesn’t work well, or the theme is not responsive. In mobile responsive themes, the drop down works beautifully on just about any device… on regular webpages, there may be trouble getting them to behave properly.
My one big “pet peeve” is when there is a drop down, but the root (visable without hovering) is linked to a page directly. Most of the time when using an iPhone or Android you tap the menu’s root and thus highlight/hover. When I do this and it navigates me away, it make the menu pretty useless, and it makes me frustrated. Then I have to go back and long press on the menu, cancel the popup for extra options, and it will finally extend allowing the selection of items inside.
tip: spiders crawl the top of the menu list first, and thus give those linked pages a higher priority 
arranging drop down menus in a fashion that allows indexing is important. Do not use .JS (javascript is not search friendly) menus if possible as the internal linking they create is important for optimization.