Russia is a country with a rich history and there are many causes for celebration. Traditional holidays, old Soviet holidays and new democratic Russia holidays.
New Year's Day - January 1,2
Russian Orthodox Christmas Day - January 7
Old New Year's Day - January 13
Defenders of the Motherland Day - February 23
International Women's Day - March 8
Easter - April 27 (2003)
International Labor Day/MayDay/Spring Festival - May 1,2
Victory Day(1945) - May 9
Russian Independence Day - June 12
Day of Accord and Reconciliation (formerly a day of the October Revolution) - November 7
Constitution Day - December 12
Wondering why Russian Christmas comes after the New Year and what is the "old new year's day"? Apparently, Russian Orthodox Church was so orthodox than when the country adjusted its calendar along with the rest of the world in early 20th century, they refused any change and forced religious Russians to observe Christian holidays according to the old timeline. There have been some discussions about finally giving in to progress and changing the church holidays but it has not taken affect yet.
As of now, Russians start celebrating with the rest of the world on December 25 and do not stop till January 13. Great time for pleasure trips but stay away if you are traveling on business. You won't get anything done. If you travel to Moscow around Christmastime, you would be able to enjoy public concerts and Red Square champagne celebrations. May Holidays and the former Revolutionary holiday is the time to see the old Soviet guard march on the streets with the old slogans and sometimes, even portraits of Joseph Stalin.
There is usually plenty of police around and you can safely watch the spectacle but I would not recommend getting into discussions over the benefits of the capitalist system with any of the angry participants. The new Independence Day holiday commemorates the break down of the Soviet Union and the formation of new Russia. It should really be an Independence Day for all the former Soviet republics who were under the Russian rule but who am I to deny a bit of political correctness. There will be concerts and celebrations on the streets sponsored by the Moscow government.
All public offices are closed during the official holidays. Some embassies close down as well but you would be able to get in touch in case of emergency. Most stores close but this should not affect souvenir shopping since vendors usually hurry to take advantage of the crowds