The newer audio (starting with 2010) are available on the Supreme Court's website. Older arguments are available at www.oyez.org. Oyez page shows the written transcript of the oral arguments as well as the audio recording. While this is wonderful for listening to the audio on the computer, the page has no feature to download the audio file.
(I found a page which explained how to access the audio file (mp3) directly. This involved entering the URL for the source file, which follows a certain formula based on the case number and the URL of the Oyez page. Alas I have forgotten how to do this.)
Does anyone know... How can the audio file be accessed to save or copy? UPDATE: Apparently there is indeed an download feature. Maybe this is a new update?