Many courts now post copies of their recent opinions on the court's website, but generally they are not designed as searchable databases of caselaw. They are great for locating the text of a known case, but not for finding cases on a specific topic.
Google Scholar, in addition to being a great place to search for scholarly articles, has the text of many court opinions. The Google Scholar database includes the following court opinions:
Google Scholar defaults to searching all federal and state courts, but after entering your search your can narrow your results by jurisdiction and date.
FastCase provides a limited database of free caselaw via the Public Library of Law that includes most cases from the U.S. Supreme Court and Federal Courts of Appeals and cases from state courts going back to 1997.
FastCase also has a iPad free app that allows you to search their database of caselaw and statutes, even without a subscription to their commercial service. If you don't have an iPad, members of the Illinois State Bar Association receive free access to FastCase as part of their membership.
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. FindLaw's content includes:
FindLaw has two primary ways to access the collection of case law. Researchers can either (1) run a search for case summaries or (2) select a jurisdiction to browse applicable laws (scroll down to click on a jurisdiction).
Google Scholar does not include a citator like Shepard's or KeyCite that informs you if the case has been overturned. It does include a How Cited feature where you can see all of the cases that cite to the original case. This is a great tool for finding additional cases that are relevant to the issue you are researching.
The How Cited feature displays previews of the language from the citing cases. Under Cited By, the bars next to the case name tell you the depth of treatment of the citing case, but this feature does not tell you whether the discussion is positive or negative.
As a final step of your research plan, it is a good idea to update the authority you are relying on by using a commercial citator like Shepard's or KeyCite.