The answering machine (or in telecommunications jargon the TAD, telephone answering device) was invented in 1912 by Roman R. Gonsett in Edmondton, Alberta, Canada. The invention was not patented. Photographs of this device exist. It appears to use a wax cylinder (similar to early phonographs).

In 1937, Bell Telephone invented an answering machine with magnetic recording, but it was only R&D. A commercial product was never manufactured.

September 27th is supposedly "Answering Machine Day" because there is a story that the invention of the answering machine happened on this date in 1950.

Years later in 1968 a garage-based operation named TronTech would create an electronic answering machine that used reel-to-reel tape. In May of 1971 they changed their name to PhoneMate, Inc. and marketed the first commercial answering machine. I believe they patented it.

Around the web, I have seen some dates stating the invention of the answering machine ocurred in the year 1904. I cannot verify this statement however. Due to the lack of who, when, where, and how I will only note it here.