In an emergency situation, the cellular network may be extremely congested or lose power completely. Some AM/FM radio stations have backup power (TODO — roughly how many?), but eventually their fuel or batteries will run out. It's useful to have minimal contact with the outside world, and shortwave stations can be heard from several thousand miles away, making them an attractive fallback option.
You can get a cheap shortwave-capable radio on Amazon for perhaps $20. But there's a problem — RFI/QRM (radio-frequency interference) is fairly strong in the urban environment, and RFI plays havoc with shortwave listening (SWL).
In a rural area, it's totally reasonable to string up a random-wire antenna in a tree (AKA a "sloper"), with an alligator clip attached to the cheap radio's telescopic antenna. And, even in an urban area, if most people lose power, then RFI/QRM should die down.
BUT... if you live in an urban area, you will want to practice with shortwave listening ahead of time, so you have the skills ready for when SHTF.
To deal with RFI in the urban environment, you'll want 1) a decent-quality radio that is well-shielded, and 2) a good antenna. A very popular antenna option for shortwave is an active-loop antenna. One mag-loop antenna I'm interested in is PK's Loop Antenna [PK's eBay store] [reviews] [manual].
Personally, SDR (software-defined radios) really appeal to me, and they've gotten a lot better in recent years. And if it could be done on an Android phone, to make it portable, even better.
Solutions for Android SDR software:
Specific hardware that interests me includes the RTL-SDR dongle.