Like most countries, Japan has a long list of holidays. Here are brief descriptions of the major ones. Note that virtually every town and city in Japan also has a local festival or two of its own at some point during the year, but I’ll talk about them another time.
First off, the only US holidays that are widely celebrated in Japan are Halloween, Christmas, and Valentine's, although they're observed a bit differently than in the US or Europe (more on that in a minute). Holidays like Thanksgiving and the 4th of July naturally aren't celebrated in Japan (or anywhere outside of the US) because they're tied into US history. I assume Easter is observed by Japanese Christians, but they're a pretty small minority so I'd be surprised if most Japanese people even know what Easter is.
New Years is a major holiday but it's observed differently in Japan than in the US and Europe and it’s kind of an international thing anyway.
Now, for a quick (well, somewhat quick) list of major Japanese holidays. All holidays on this list, national or not, are widely observed but national holidays are ones officially sanctioned by the government (and ones that many businesses close on). Non-national holidays are identified as such. It’s also worth noting that the dates of some of these holidays were changed fairly recently to give people more three day weekends.
New Years Day (late Dec - early Jan):
New Years in Japan is focused more on resting and family than partying. Many people dress in traditional clothes and visit shrines to pray and get their luck predicted for the new year. Traditional foods include special kinds of noodles and mochi (a gluttonous rice substance). Quite a lot of businesses shut down for several days during this period, sometimes starting as early as the 29th or 30th and going till anytime between the 2nd and 4th. The first week of January, when the stores re-open, is the biggest shopping time of the year, with stores of all types having major sales and selling mystery grab bags containing a random mix of items worth far more than the cost of the bag.
Coming of Age Day (2nd Monday of Jan):
This holiday celebrates people who recently turned 20. These new adults dress up (often in traditional clothing) and attend a speech by city officials about the importance of being responsible individuals. They then go off to party.
Setsuban (Feb 2):
Setsuban celebrates the start of spring, though it’s not a national holiday. Popular traditions include eating soy beans and throwing them at people wearing oni (monster) masks to chase out evil spirits.
National Foundation Day (Feb 11):
It commemorates the establishment of the nation. Like Columbus Day, people don’t really celebrate it so much as appreciate the day off.
Valentine's Day (Feb 14):
Though not a national holiday, Valentine’s is quite popular but it works a bit differently than it does in the US. In Japan, it's a day when women give chocolate to men they like as well as to male friends and coworkers. There are actually different names used for the chocolate depending on if it's being given in a friendly or romantic spirit. The nicer the chocolate, the more the girl cares about the guy, with homemade chocolate being the most romantic.
Hinamatsuri (Mar 3):
Hinamatsuri or Girls’ Day isn’t a national holiday. On it, girls display a fancy (and expensive) set of dolls.
White Day (Mar 14):
This counterpart to Valentine’s also isn’t a national holiday. It's Valentine's Day all over again except this time it's the guys' turn to buy things (often candy or jewelry) for the girls that gave them chocolate on Valentine’s. As an interesting note, the holiday was actually established by Japan's national association of candy makers.
Vernal Equinox (sometime in Mar):
A holiday for the equinox. There’s no real celebration, but it’s a day off of work/school.
Hanamatsuri (Apr 8):
This Flower Festival celebrates flowers and the birth of Buddha. It’s not a national holiday.
Golden Week (Apr 29 - May 5):
A week long holiday period encompassing four separate holidays. School and many businesses close for the entire week. It’s a very popular time for tourism, with hotels in popular locations often being booked solid months in advance. The four holidays are as follows:
Showa Day (Apr 29)
It celebrates the birthday of the Showa Emperor.
Constitution Memorial Day (May 3)
It commemorates the Japanese constitution.
Greenery Day (May 4)
More or less equivalent to Earth Day.
Children's Day (aka Boys' Day) (May 5)
This holiday has its own set of dolls different from the Girls' Day ones and is marked by flying large koi shaped streamers.
Tanabata (in Jul or Aug, exact date varies by location):
The Star Festival. It’s based on the ancient myth of the lovers Orihime and Hikoboshi (the stars Vega and Altair). People celebrate by having festivals, setting of fireworks, and tying cards with wishes written on them to bamboo stalks. It’s not a national holiday.
Marine Day (3rd Monday of Jul):
A rather new holiday that celebrates the ocean.
Obon (Jul or Aug 13 - 15 depending on the location, Aug is more common):
Though it’s not a national holiday many businesses still close for Obon. It's marked by people traveling to their ancestral homes to visit their family tomb and pray to the spirits of their ancestors. The exact celebration details vary by location.
Respect for the Aged Day (3rd Mon of Sept):
The name says it all.
Autumnal Equinox (sometime in Sept):
The counterpart to the Vernal Equinox holiday.
Health & Sports Day (2nd Mon of Oct):
A holiday to promote fitness and personal wellbeing.
Halloween (Oct 30 or 31, some people get the date mixed up):
Halloween isn’t a national holiday and there's no trick or treating or any real celebration (aside from some costume parties). Halloween decor (ghosts, pumpkins, etc.) and candy are fairly popular though, especially among kids and young adults.
Culture Day (Nov 3):
Culture Day celebrates the Japanese constitution (again) and the Meiji Emperor's birthday.
Labor Thanksgiving Day (Nov 23):
This one is somewhat similar to Labor Day in the US but without any real celebrations or parties. It has no relation to the US Thanksgiving Day holiday (though Japanese people tend to confuse the two).
The Emperor's Birthday (Dec 23):
The birthday of Emperor Akihito (the current emperor).
Christmas (Dec 24 - 25):
Despite the small amount of Christians in Japan, Christmas is still widely celebrated, though not as a national holiday. Santa, presents, carols (in Japanese), and lights are all popular but trees are bit less common than in the US and Europe because of the limited space both to grow and display them. Outside for the aforementioned Christian minority, the holiday is purely secular without nativity scenes, angels, or any references to the birth of Jesus. Christmas Eve is actually far more popular than Christmas itself and is a very popular time to take your significant other out for a romantic evening.