I have a DSL line. The only way to get a DSL line around here is to have a POTS line. I don't really need it for anything, I can't even remember the number, but there it is. I have an old-fashioned line-powered phone, with a mechanical ringer no less, attached to it so that if my parents need to reach me in the middle of the night -- they're both elderly, and emergencies can happen -- they can call that number and it will definitely wake me up. Nobody else has that number and nobody should be calling it.
But, of course, wrong numbers happen, and everybody gets calls for the previous owner of whatever their number is. So it actually rings several times a week. I ignore it, because I know my parents will try my cell phone first, but it's always nerve-wracking, because maybe the reception is bad or something and it is them... or maybe it's the new phone company calling to tell me that I'm going to be charged five billion dollars a month for this line, and not screaming "oh god no" within the next five seconds constitutes acceptance of the new terms... Anyway, with an answering machine I can screen the calls and safely ignore the ones which are safe to ignore. And I can come home and find messages which were left despite an announcement saying that messages would be laughed at and ignored, and laugh and ignore them.