Festivals are more family affairs in Beijing, which doesn't have much of a calendar of public events compared with some other parts of China.
For an exhaustive list of events beyond those listed here, check http://events.frommers.com, where you'll find a searchable, up-to-the-minute roster of what's happening in cities all over the world.
Spring Festival (Chun Jie), or Chinese New Year, is still the occasion for large lion dances and other celebrations in Chinatowns worldwide, but in mainland China it's mainly a time for everyone to return to his or her ancestral home and feast. Fireworks are now banned in Beijing; however, temple fairs have been revived but are mostly fairly low-key shopping opportunities without much of the color or professional entertainers of old. But in the countryside, there's been a gradual revival of stilt walking and masked processions. New Year is on the day of the first new moon after January 21, and can be no later than February 20.
Lantern Festival (Deng Jie) perhaps reached its peak in the late Qing dynasty, when temples, stores, and other public places were hung with fantastically shaped and decorated lanterns. Many people paraded through the streets with lightweight lanterns in the shapes of fish, sheep, or other animals, and hung others, often decorated with riddles, outside their houses. There are modest signs of a revival. This festival always falls 15 days after Spring Festival.
Tomb-Sweeping Festival (Qingming) is frequently observed in Chinese communities overseas, and more often in rural areas of China, as a family outing on a free day near the festival date. It's a day for honoring ancestors by visiting and tidying their gravesites, and making offerings of snacks and alcohol, which often turns into a picnic. It is now an official holiday and people usually get a long weekend. April 4.
The last remnant of the Mid-Autumn Festival (Tuanyuan Jie), except among literary-minded students, is the giving and eating of yuebing (moon cakes), circular pies with sweet and extremely fattening fillings. Traditionally it's a time to sit and read poetry under the full moon, but pollution has made the moon largely invisible. Like the Tomb-Sweeping Festival, this is now an official holiday and companies usually grant a 3-day weekend. Takes place the 15th day of the 8th lunar month (usually Sept).
National Day itself is for avoiding Tian'an Men Square, especially if the government considers the anniversary important enough for one of its military parades, when the square may be blocked to you anyway. October 1.
Note: This information was accurate when it was published, but can change without notice. Please be sure to confirm all rates and details directly with the companies in question before planning your trip.