Real example: I'm collecting some quality signals from a corpus, most of which are some form of ratio, average, weighted average, or scaled average of counting various quantities within the documents. If the elements being counted are missing, I want the term involving that quality signal to disappear from the final ranking calculation.

Defining x / 0 = 0 gets this behavior for free, while leaving zero as an exception means it has to be caught for every single signal calculation, which is a pain when there are potentially dozens of different signals, all of which are counting different things (and have different divisors). I've actually defined a helper function to do this automatically, which also lets me change the default "null object" easily if I choose a different representation or want to apply some baseline value.