In 1962, Arthur C. Clarke was touring Bell Labs when he heard a demonstration of a song sung by an IBM 704 computer programmed by physicist John L. Kelly. The song, the first ever performed by a computer, was called "Daisy Bell", more commonly known as "Bicycle Built for Two" or "Daisy, Daisy". When Clarke collaborated with Stanley Kubrick on 2001: A Space Odyssey, they had HAL sing it while Dave powered him down.
A clip of a 1963 synthesized computer speech demonstration by Bell Labs featuring "Daisy Bell" was included on an album for the First Philadelphia Computer Music Festival. You can listen to it (it's the last track) and the rest of the album at vintagecomputermusic.com. (via mark)
Update: A reader just reminded me that HAL may have been so named because each letter is off by one from IBM, although Arthur C. Clarke denies this. (thx, justin)