Nara's deer are famous for "bowing" to people to ask for food. This is a learned behavior unique to this park.
The Trick: If you bow to them, they will often bow back.
The Warning: While they are polite, they can get impatient! If you show them a cracker (shika senbei) but don't give it to them quickly, they might nudge you or gently tug on your clothes.