Every culture has superstitions, many of which seem to not make sense. Looking at the origins of the superstition and a great deal of them do make sense in some context. Here are a few Japanese superstitions, there are more, and there are also quite a few region specific superstitions (i.e. local ones not found throughout the country, not listed):
*It is thought that when someone sneezes (Kushami), someone is talking/gossiping about that person. Additional comment - In Japan when a person sneezes it is not common to say god bless you, bless you, or Gesundheit.
*If a kamidana (miniature Shinto shrine) falls it is an omen that a bad thing is, or will, happen.
*Breaking a comb or the cloth strap of a geta breaking is an omen of misfortune.
*You should never write a person's name in red ink, unless your trying to curse them.
*The crow is considered an evil omen and bearer of bad luck. Loud crowing or the gathering in large numbers is a sign of disaster, particularly in the evening. The thing is not all crows are considered bad luck, some crows are viewed as the messengers of the kami, a single crow cawing at 6 am and noon is good luck, and it is thought that crows take care of aged parents.
*It is thought that if you give someone your cold it will cure yours. It is also thought that stupid people don't get colds hence Ranma's comment about not thinking Tatewaki Kuno could get one.
*If you whistle in the night, a snake (or a thief, or a ghost) will come to you.
Many Japanese superstitions show up in the Ranma manga, as the above pictures show. Knowing the superstitions, is somewhat helpful when reading manga or watching anime, since some are clearly foreshadowing, and/or an explanation for persons actions. Knowing them can give you an idea as to where the author got the idea from.