Answer:
According to the US Census, San Fransisco, San Jose, and Oakland are all considered in the Bay Area.
However, according to the Association of Bay Area Governments; Sonoma, Napa, Salono, Marin, Contra Costa, San Mateo, Almeda, and Santa Clara counties are all members. This includes 7 million people, nine counties, and 101 cities.
http://www.abag.ca.gov/overview/aboutbayarea.html