To me, the Bay Area is defined by how far people will commute for a job. In my mind, San Jose is part of the Bay Area because a number of my coworkers live there or in Sunnyvale / Santa Clara, and yet work across from the Ferry Building in downtown SF.

I would say Marin area, all the way south to San Jose, all the way up through Fremont, then Oakland, Berkeley, etc... I have only lived here for 4 years, but that is what I consider to be the bay area.

Some info from Wikipedia

The San Francisco Bay Area, commonly known as the Bay Area or simply the Bay, is a metropolitan region that surrounds the San Francisco and San Pablo estuaries in Northern California. The region encompasses large cities such as San Francisco, Oakland, and San Jose, along with smaller urban and rural areas. Overall, the Bay Area consists of nine counties, 101 cities, and 7,000 square miles.[3] The nine counties are Alameda, Contra Costa, Marin, Napa, San Francisco, San Mateo, Santa Clara, Solano, and Sonoma.[3][4]

The Bay Area when defined as a Combined Statistical Area, is the sixth largest in the country, with approximately 7.4 million people.[5] It encompasses the metropolitan areas of San Francisco (12th largest in the country) and San Jose (31st largest in the country), as well as four other smaller, surrounding metropolitan areas. The Bay Area hosts many cities, towns, military bases, airports, and associated regional, state, and national parks, connected by a massive network of roads, highways, railroads, bridges, tunnels and commuter rail. The combined urban area of San Francisco and San Jose is the 46th largest urban area in the world.

San Francisco is the cultural and financial center of the Bay Area, and has the second highest population density of any major city in North America after New York City.[6] San Jose is the largest city in terms of population, land area, and industrial development. Oakland is a major manufacturing and distribution center, rail terminus/hub, and has the fourth largest container shipping port in the United States. The Bay Area is renowned for its natural beauty, liberal politics, affluence, diversity, and new age reputation.

I think a section that kind of gets forgotten in the "Bay Area" is up above Berkeley in Benecia and Vallejo area as well. The different areas of the Bay are very different and dynamic because of the simple fact that it is a cultural and financial hub. This also makes it hard to solidify an internal cohesive identification that can make me say "I'm from the Bay Area." (It's also hard to identify this because I don't know what I identify with here because I haven't lived anywhere else long enough to know when I am missing it.)

My definition of "The San Francisco Bay Area" is San Jose to the South, Vallejo to the East, and Novato to the North. Basically, anywhere that San Francisco Bay borders. Beyond Vallejo you go through the Carquinez strait into Suisun Bay (not SF Bay). I realize that technically that northern area is San Pablo Bay, but Point San Pablo is not nearly so much a physical separator as the Carquinez strait.