The Supreme Court Briefs page on Findlaw provides access to U.S. Supreme Court briefs going back to the 1999 term. To access the briefs for a particular case from this website, first choose the term in which the case was heard, and then look for the name of the case from the alphabetical list provided. When you click on the case name, you will be provided a statement of the questions presented in the case, as well as links to relevant documents, including petitions and briefs filed at the various stages of the process.
Keep in mind that this website only offers selective coverage of petitions and briefs. Therefore, for some of the cases listed for each term, you may find only a limited number of briefs (or none at all).