I was a contributor to the problem, though, in that while I didn't have an answering machine, I did have a modem: 300-baud beast that you had to manually connect once your phone dialed the number - just once step up from acoustic couplers.
It was 1990. I was boarding in a dank basement room here in Winnipeg while I worked at my summer job. But yay, I had my own phone line. So off to the store I went, and I bought my first answering machine! It used real cassettes, too, not these mini things, so I could record my outgoing message on my stereo. Talk about fun! I used this really, really bad rendition of the theme music to 2001: A Space Audacy. I don't know what that song is, no doubt the lovely FunBlindSinger would know. Anyway, this was an absolutely horrid rendition by a group called the Portsmouth Symphonia. I added a little diabolical laughter, some reverb, and all in all was darned proud of my efforts. My faith in the fruits of my labor was validated some weeks later when I got the following message on my machine: "Hi, this is a wrong number, but I loved your message!"
Through the years I tried other original messages: a standard greeting with the Dudley Doright theme in the background ("Hmmm, I bet that's Rod [my roommate] on the trumpet, right?"), a Valentine's Day message with a little ditty called Tapeworm of Love in the background (I won't quote what the wrong number caller on my machine said to that one), and others. One time I had a friend of mine record my outgoing message for me in the sultriest of voices: she sounded positively naked. This went over great, until my mom called me and, shall we say, voiced extreme displeasure over my choice of outgoing messages, insisting that I remove the outgoing message immediately. I did have the good sense to keep the tape. Oi, what fun, I absolutely love answering machines!