When we returned to no power in Florida after the big hurricanes, the land line phones still worked -- go figure!
Jay
On plain old telephone service (POTS), power for the phone is supplied over the telephone line itself - 48 volts DC. In fact, that's how the telephone company detects that you've picked up the phone - you connect the circuit and current flows through the one wire, through the phone, and back through the other wire. There's not much power in that "local loop" (as the telephone people call it), but there's enough to power a simple phone. When a call comes in, a much higher AC voltage is applied to the loop, which rings your phone. In the early days of telephones, that AC signal drove an electromagnet which in turn drove a clapper on a bell. Modern day phones use a much less power hungry system to power a speaker which emits an electronic sound.
The telephone company has big racks of batteries to supply this DC power, and also to power all the electronic equipment in the central office (CO) - almost all electronic equipment that is to be installed in a CO has to run on negative 48V DC. For most COs the batteries will last quite a few hours but they all have diesel generators to provide power through long periods of power outs. If you are ever interested, contact your phone company and ask for a tour of your local CO. It's easiest to get a tour if you're part of some local community group - they generally won't do a tour for one person (unless you know someone who works in the CO). Since 9/11 they've tightened up on tours - used to be very easy to get in.
That's why your phone works when everything else that requires power is gone.
But you have to do your part. If you have cordless phones, you have to provide power to the base station so that the phone still works. Better yet, buy one cheap corded phone and put it in a room that you don't use much. When the power fails and your cordless phones no longer work, your cheap corded phone will still provide you service.
More than you ever wanted to know about your telephone system!
Mike
PS - a lot of telephone service is provided through digital loop carriers (DLCs) now and not directly from a CO. If you'd like to know about DLCs and how they work, I'll be happy to really bore you. Ask me about optical networks some time when you can't get to sleep and I guarantee I'll cure you.