Google Scholar has recently begun offering free access to federal and state case law (as well as some law reviews and other secondary legal materials). You can access U.S. Supreme Court opinions from 1791 to the present and other federal opinions, including district, appellate, tax and bankruptcy opinions, from 1923 to the present. State appellate court cases are available from 1950 to the present.
You may search for cases the same way you search for any information on Google. Using the advanced search option, you can restrict your search to federal or state court opinions. For more information, see the discussion at the Google blog. You may also want to see Google Scholar: A New Way to Search for Cases and Related Legal Publications.
Remember, there are a number of other very good sources for free cases (and more), including: Lexisone.com, Precydent, and The Public Library of Law. Caution: None of these sources is yet comprehensive and you should always check the scope (jurisdictional, geographical, and chronological) of their coverage.