Among the holidays in the United States and Japan, there are only two that are on the same dates. And they both are in the month of January. One of them is, of course, January 1, New Years Day. The other is January 15. In Japan this is "Adult Day" (sometimes translated as "Coming of Age Day.") In America, this is Rev. Dr. Martin Luther King, Jr.'s Birthday.
In America the representative holidays are Independence Day (July 4) and Labor Day (first Monday in September). In Japan you have such holidays as Vernal Equinox (March 20), Constitution Day (May 3), and new from last year, "Ocean Day" (July 20). Also, both countries have holidays to honor those people we respect. For example, President Washington's birthday and President Lincoln's birthday are both in February, so America has a joint celebration called Presidents' Day (the third Monday in February). In Japan there is the Emperor's Birthday (December 23) and also Emperor Showa's birthday (April 29) became "Green Day" and Emperor Meiji's birthday (November 3) became "Cultural Day."
In America Rev. King's birthday became a holiday several years ago. Dr. King worked for the US Civil Rights movement, seeking equality for Black Americans using non-violent means. In 1964 the federal Civil Rights Law was passed, and after that Black Americans joined US society in a more obvious and fair way; many more Black mayors, for example, were voted in after the law was passed. Dr. King was awarded the Nobel Peace Prize in 1964 for his efforts. Dr. King had many White supporters, but in 1968 he was felled by a radical's bullet.
Every year on Dr. King's birthday there are speeches and parades organized to raise peoples' consciousness about working to protect peoples' basic civil rights. The movement is to stop discrimination on the basis of what color your skin is. It is similar to Japan's "Human Rights Day" activities, I think. When I was in college I would participate every year in the parades.
In the sixteen years since I wrote this, there have been a few changes on the Japanese side. Japan as a country finally adapted the idea of moving most holidays to Mondays so that people could have three day weekends. (They called the movement "Happy Monday.") So that was a step forward. However, the Emperor Showa (known internationally as Emperor Hirohito) is being celebrated now that he has been dead long enough; the first few years after his death his birthday was celebrated as "Ocean Day" but now it has been re-named Showa Day. The Japanese government seems intent on wanting people honor the dead man, even though he personally hated the cult of personality that sprung up around him and his family before him. Showa, by the way, is the name of his reign. The current Emperor is called "Heisei."
Here is a list of the current Japanese holidays:
New Years' Day (Jan 1)
Adult Day (2nd Monday in January; used to be Jan 15)
Foundation Day (Feb 11; the day the god-emperor Jimmu acceded to the throne of Japan, thereby creating the country)
Vernal Equinox Day (March 20 or 21)
Showa Day (April 29; previous Emperor's birthday)
Constitution Day (May 3; the day in 1948 when the Japanese Constitution took effect)
Green Day (May 4)
Childrens' Day (Boys' Day) (May 5)
Ocean Day (third Monday in July; used to be July 20)
Respect For the Aged Day (3rd Monday in September; used to be Sept 15)
Autumnal Equinox (Sept 22 or 23)
Physical Education Day (2nd Monday in October; used to be Oct 10, which commemorated the Opening Ceremony of the 1964 Tokyo Olympics)
Culture Day (Nov 3)
Labor Thanksgiving Day (Nov 23)
Emperor's Birthday (Dec 23)
For more information, please read the wikipedia article Public Holidays in Japan.