A typical Japanese breakfast consist of at least gohan (rice) and miso shiro (miso soup). These two are the main must-have items. Along with these you sometimes also get eggs rolls, pickled vegetables, crispy seaweed, boiled vegetables and so on.
I like Japanese pickled vegetables a lot, especially those that are lightly pickled. My favourites are pickled seaweed, lotus root and radish.
There is usually also something else served during breakfast - Natto (納豆). Natto is fermented soybeans with a very strong cheesy smell. It has been liken to stinky tofu and durians. It is very well-liked by many Japanese although many foreigners have been known to be put off by it. It has the consistency of a glue-stick and you usually mix in some soy sauce and musturd, stir hard and then eat it with rice. (See this picture from wikipedia for details)
I used to find natto scary and quite gross.. but the ready-made ones in a cup (you can find these in the supermarket) taste quite unremarkable to me.
Japanese breakfast at the first Ryokan. Japanese grilled fish
(fish grilled with very little salt) is very yummy
Japanese breakfast at the Urashima Hotel. Natto is the thing in the little red cup..