The Oyez Project website has a multimedia archive of the US Supreme Court.
Since October 1955 virtually all the Court’s sittings have been recorded. The Oyez Project has been going some time now, and already allows anyone free access to more than 5000 hours of the audio tapes from the period 1981-2007, and a selection of pre-1980 tapes – totalling over 5000 hours already. The aim is, of course, to have all the historic tapes available in due course – and to keep the library going as new cases are recorded.
Legal historians interested in earlier periods need not feel ignored – the website also summaries and links through to transcripts of Supreme Court cases reaching back to the eighteenth century.