I often get asked where to find API data for Beijing. So here goes:
The easiest place is the home page of the Chinese Ministry of Environmental Protection: www.mep.gov.cn (Chinese), english.mep.gov.cn (English). Complete data for all cities in China is available here, http://datacenter.mep.gov.cn/TestRunQian/air_dairy.jsp, but only in Chinese. This page is often updated before the Ministry's home page. Archived data is searchable at top of the same page, but again only in Chinese.
Above paragraph updated to reflect new location of complete air quality dataset. More information here and here.
The API is usually updated daily by MEP around 2-3pm each day. However, this is not always the case. Occasionally, like yesterday, the data will be mysteriously delayed or not reported at all. Sometimes, the Chinese site will be updated, but not the English site (as of 6:00pm on 7/29, the MEP English home page still only reports data from 7/23).
An alternative source for API data is the Beijing Environmental Protection Bureau's air quality page, http://www.bjepb.gov.cn/air2008/olympic.aspx, in English and Chinese. The Beijing EPB provides individual readings of meters across the city, but no single average number.