One of the Law Library of Congress's recent blog posts pertained to finding free case law on the Internet.
As the post points out, "[o]ne of the defining features of the common law system is the emphasis placed on the precedential value of case law. Until recently, case law has not been widely available on the Internet, leaving researchers with no choice but to seek out print reporters and commercial electronic databases to locate cases of interest. This situation has started to change, however, and now researchers have several free, online databases at their disposal."
Generally, free databases on the Internet only contain the text of the opinion and do not contain the valuable annotations that aid in research, but these databases are a starting point.
The free case law databases that the blog post specifically mention are:
Google Scholar offers an extensive database of state and federal cases.
FindLaw offers a database of case law from the U.S. Supreme Court and U.S. Circuit Courts of Appeal, as well as several state supreme courts.
Justia offers cases from the U.S. Supreme Court, U.S. Circuit Courts of Appeal, and U.S. District Courts. Additionally, you may find links to many state supreme court and intermediate court of appeal cases.
The Public Library of Law (PLOL) offers cases from the U.S. Supreme Court (1754-present), U.S. Circuit Courts of Appeal (generally 1951-present, with a few exceptions), and state cases (1997-present).
And as I've mentioned before, many state bars offer a free case law database to their members.
Most of these databases will have their own specific advanced searching techniques, so make sure to check out the 'help' function on each database for more information.