In 1985, Radio Shack had an answering machine that played a series of cheesy songs to the listener about how they were unable to get to the phone. It's been preserved in a cassette and uploaded to youtube for your enjoyment. There are so many groovy songs on here that I can't decide which one is my favorite.
From the YouTube description:
"Telephone Answering Machine Outgoing Messages: Music Edition" was produced and published in 1985 by Radio Shack, a division of Tandy Corporation, and has a catalog number of 43-417.