With the intention to "find out". It's an invasion of privacy and its none of your business. It's more of an issue of being disrespectful than actually knowing how much, because eventually it boils to having the nerve to ask someone with no other intention than to find out how much they earn compared to themselves, and being comfortable enough to ask such a personal question, especially when you're only supposed to work and not discuss earning.
I believe it is fair for someone in the same work area to ask about your income, they may just want to know if they are getting paid correctly and they will usually be sharing about their income as well. Rude is an exaggerated word to use, it should be changed to unprofessional.You should only feel offended if you get paid dreadfully (;