Good lord, many. There's the Bon Festival, Boy's Day/Hinamatsuri, "Golden Week" (analogous to the US President's week), and something now called Labor Thanksgiving Day which was based off of ancient harvest festivals. These festivals, while not abandoned, were "adapted" to Western standards after the Meiji Restoration as well as World War II. As many of these festivals were based off a lunar calendar prior to the transition to a Gregorian one, their dates also changed, and were made public, state-wide holidays.

You do have to keep in mind that Japan is quite a large country, and that different regions also had their own regional holidays, or how they celebrate the holiday may differ as well (Kanto vs. Kansai being the most obvious example).

Could you clarify what you mean by "analogous to Christmas or Halloween"?