The U.S. Supreme Court website has made the transcripts (beginning October 2000 term) and recordings (beginning October 2010 term) of oral arguments heard by the Court available for free on their website.
The website also includes information about availablity of earlier transcripts and recordings and a vistor's guide to oral arguments.
Briefs for the current term of the U.S. Supreme Court are made available through the American Bar Association. Links to bound volumes (1991-date), slip opinions (last several years), biographies of the justices, and a great deal more can be found on the website.