There's a way of asking questions that's more common when being especially formal; in fact, in some cases using it just comes across as stuffy:

"Have you no shame?" is more formal than "Do you not have any shame?", which is more formal than "Don't you have any shame?"

"Hath not a Jew eyes?" is more formal than "Does a Jew not have eyes?", which is more formal that "Doesn't a Jew have eyes?"

The second one is actually a Shakespeare quote ("hath" became the Modern English word "has", as in "he has"), which makes it more common, but otherwise sentences like above can sound overly pompous.

Also, see dangling prepositions ("What are you afraid of?") and, to a lesser extent, split infinitives ("to boldly go where no man has gone before").