"The Oyez Project is a multimedia archive devoted to the Supreme Court of the United States and its work." It covers all audio from the 1970 term forward, and selective audio coverage from 1955 to 1970. Note that their main focus is audio materials, but they provide abstracts for a portion of cases, and links to opinions "in every case decided by the Court back to 1793."
This website provides an interface to a database of information about Supreme Court cases back to the 1946 term. The database contains 247 pieces of information for each case which can be used to "...directly calculate and view relationships among the variables in the database." According to the website, this data set has been used for "...virtually all systematic analyses of the contemporary Supreme Court."
Covers Supreme Court opinions from 1791 forward and Federal Appellate Cases from 1951 forward, and Federal District Court cases from various years. You can select by court, and then year. There is a search box at the top, but it searches the entire site rather than just the cases
"Public Access to Court Electronic Records," and it is "an electronic public access service that allows users to obtain case and docket information from federal appellate, district and bankruptcy courts." Not a free service, but not very expensive.