Not only is Oyez the "authoritative source for all audio recorded in the Court since the installation of a recording system in October 1955," it also has: news; analysis; information about the court, its opinions, and its justices; and a Podcast of newly-added media.
Coverage begins in October 1979. Transcripts are available as soon as they are released to the public. Use the "Search within results" box on the left-hand side of the screen to find opinions by key word, docket number or party name. Follow these examples for docket number or case name searches:
number(12-307) name("united states" and windsor)
Oral Argument Transcripts on Microfiche
The Zief Law Library has oral argument transcripts from 1969 to 2016. They are filed by docket number in Fiche Cabinet 20, drawer 7. The set contains all transcripts for review granted cases.