Learn Russian: Ни пуха ни пера! — К чёрту! - Break a leg!

Literally, it means neither down nor feather. It originated as a phrase said to hunters. People believed that wishing a hunter good luck would attract the attention of evil spirits who would ruin the hunt. By wishing the hunter no down (meaning no furry animals) and no feather (meaning no birds), they hoped to trick the spirits. Today, it is heavily used to wish someone good luck before an exam or a big interview.

Why are пуха and пера in the genitive case?

In Russian, when you wish for something to be absent (or pretend to, as in this idiom), the noun takes the genitive case. Since ни ... ни ... (neither ... nor ...) expresses a strong negation, the original nominative words пух (down/fur) and перо (feather) become пуха and пера.

Normally, the ни ..., ни ... construction requires a comma. Why is there no comma here?

You are right that Russian punctuation rules generally require a comma before the second ни in a list. However, there is a specific exception for fixed idiomatic expressions. Because ни пуха ни пера is a highly standardized set phrase, the comma is always dropped.

Can I respond to this with Спасибо instead of К чёрту?