This article is on the same subject: it describes what AT&T has been telling people about the need to keep landlines for ther own safety. Some of the above posts make similar points.
http://www.betanews.com/article/ATT-Without-a-landline-phone-you-could-die/1247069154
However, that's really part of an advertising strategy, and perhaps a desperate one. AT&T has another point of view on this: with the increasing rate at which customers are abandoning landlines, the remaining customer base is becoming insufficient to justify the high costs of maintaining the landline infrastructure. They are pressing regulatory bodies to permit them to shut down landline service altogether.
http://arstechnica.com/telecom/news/2009/12/att-landline-phone-service-must-die-only-question-is-when.ars
My next door neighbor had his telephone service provided by his cable TV provider. When storms took out power in the area a few summers ago, he was out of luck--for several days. By the way, our cordless phones didn't work either, but we had retained one of the old phones that did work.
Of course, telephone lines can be knocked down, too.
A couple of year ago on PDTV, Mas Ayoob suggested that people consider having two cell phones from different service providers in case one goes down. Sound extreme? Well, until recently, I had a car with On*Star, and the satellite phone on it worked when cell phones did not.
A satellite based phone working through an IP provider just might be in all of our futures, for the reasons set forth in the second link above.
The biggest risk would seem to involve power outages. When one thinks about it, a back-up generator starts sounding like a good idea, As a matter of fact, I have one, but the primary reasons I put it in had to do with light, refrigeration, and temperature control.
It has worked very effectively--we haven't had a power outage in the fifteen months we've had it.
Does not having landline pose a safety problem? With those who have said yes, I have to agree, but I predict that we will all have to face that issue in the not too distant future.
Frankly, I think not having a cell phone poses a much, much bigger risk these days.
One other thing: there's the possibility of radio--one does not need to learn Morse Code these days to get a license.