The Supreme Court has transcribed and recorded nearly all oral arguments heard since 1955.
The Complete Oral Arguments of the Supreme Court of the United States (University Publications of America):
This microfiche collection contains oral argument transcripts for cases heard from 1952 to the present. It is available in the Law Library.
Landmark Briefs and Arguments of the Supreme Court of the United States (Philip B. Kurland and Gerhard Casper, University Publications of America, 1975—)
This multi-volume print set contains oral argument summaries, abstracts, and texts from selected constitutional law cases from 1793 to 1980. The set is organized chronologically, and the names and years of cases included in each volume are printed on the spine. It is available in the Law Library.
United States Supreme Court Website
The Supreme Court website has transcripts of oral arguments from OT 2000 to the present and audio recordings of oral arguments from OT 2010 to the present. Transcripts are posted online the same day as the argument, while audio recordings are posted weekly on Fridays after Conference.
Oyez has digitized hundreds of recordings of Supreme Court oral arguments from the collection of the National Archives. Selected arguments are available beginning with OT 1955 and most arguments are available beginning with OT 1979; current arguments are not available until after the term has ended. In addition to audio of arguments, Oyez has argument transcripts and provides an Oyez Player which overlays audio with text and identifies the speaker.
Westlaw (Westlaw password required)
The Westlaw Supreme Court Oral Argument Transcripts database has oral argument transcripts from 1990 to the present. Transcripts are available approximately fifteen days after the date of the oral argument.
Lexis (Lexis password required)
The Lexis United States Supreme Court Transcripts database has oral arguments from OT 1979 to the present. Transcripts are available approximately fifteen days after the date of the oral argument.