You've been getting several answers, all of which are partially correct. The answer to your question is in the link below.
To explain further: East Bay Regional Data Inc. (EBRDI) is the database provider for the Alameda County area, but brokers/agents access the data through the Paragon MLS system, which is a system provided by EBRDI that includes alot of features that agents use to enter listings and track searches, prospects, market data, and transactions.
You do have access to this system at no cost. EBRDI offers consumer access to their system at http://ebrdhomes.com/
(I've also pasted this link below).
When you go to that site, there is no "search" button after you enter your search parameters. Just hit enter on your keyboard after you've entered the last parameter and the search will begin. I just tested it, works fine and there is no cost.
As Antoine correctly points out, REALTOR.com, Trulia, and other sites may receive listings distributed from EBRDI and other MLS's, but the data that agents get through the Paragon system is much more complete than what is available on these consumer sites. I hope this clarifies things for you.