While the concept and idea of a Crystal Radio for TEOTWAWKI (no battery or external power) sounds ideal, in practice the execution leaves much to be desired.
Many ignore the fact that if a grid down situation occurs (or worse an EMP attack) that most radio stations in the affected area will be down and out for the count. In a best case scenario if the transmitting station’s components aren’t damaged, how long will their source of backup power stay up? Many modern stations rely on satellite feeds or long line telephone circuits for their program materials to be delivered and many regional stations have a minimum of technical staff (and no announcers) to maintain their operation and some station’s technical staff actually drives or travels on a circuit to do the upkeep on conglomerate owned stations in a region. US Domestic shortwave stations are in the same boat.
My point? You will probably use your radio for long distance listening to stations that are still up and functioning. Crystal radio sets run the gamut from children’s toys to hobbyist’s expensive toys but generally due to lack of amplification are useful for local listening (and some of the children’s toy type can only pick up two or three very close AM stations – even with a good (100’ long) antenna and ground).
The sets with a mechanical cat’s whisker detector are EMP  proof but the ones with a 1N34A style germanium diode are not. The junction in the manufactured diode is very, very sensitive to surges. [JWR Adds: Be sure to buy a few spare detector diodes, and keep them wrapped in insulating plastic and then in tin with a tight-fitting lid, or at least a sleeve of aluminum foil with al seams folded.]
If you want to build or use a set then my strong suggestion is to instead build a one-tube regenerative receiver  using space charge technology. These don’t require special batteries or high voltages. If you do a search for a Hiker’s Radio there are a few sites that explore the building of the sets. The component counts are low, the sets are very easy to build (only slightly more complex than a crystal radio), you can use a couple of AA and 9-volt batteries to power them and they utilize the same style of headphones as a crystal set.
The advantages are that the set can be easily built to cover the AM and Shortwave bands, the regenerative receiver can detect AM, Morse Code and SSB  signal. (In contrast, crystal radios are limited to AM only.) If built to use 12 volts DC  can be run from car batteries, dry cells or gel cell batteries. The Armstrong regenerative circuit provides amplification to the signals and you will be amazed at how sensitive the set actually is.
Parts (including the tube) are available from many sources. (You can even find the parts to build one easily on eBay). Finally, there are a few folks who build these sets and sell them on eBay. (Do a web search for “regen receiver”). Regards, – Karl A.
This is another topic about which I have some intimate knowledge. When I was a kid – when gasoline sold for 29 cents a gallon – I built three crystal radios. I build them using both a razor blade and a germanium diode as the detector. I never had a piece of galena crystal to try out.
This kind of radio receiver depends heavily on having a strong radio signal. When I built my first one my folks were living in a small town in Central Texas that had exactly two radio stations (on 1240 and 1380 AM.) I can remember hearing both stations at the same time. That was because both stations were only a couple of miles away. This is what happens when a crystal radio is used. Also, a crystal radio radio can only drive a crystal earphone, which means only one person at a time can listen to it.
Far superior to a crystal radio for survival is a pair of two superheterodyne radios. One of the two radios would be of the hand crank and/or solar cell variety, a solid state radio. Unless there is an EMP attack this will be the best radio one can have because it’s light and it requires no replacement batteries.
In case there is an EMP attack a vacuum tube radio is the best radio to have. It is possible to shield a solid state radio from EMP by storing it inside of a well grounded metal box or can. But, what if you happen to have the radio out when the EMP attack occurs? You’re SOL  unless you have a spare radio stored in a grounded can. (What if there’s a second EMP attack?)
The best type of vacuum tube radio to have is what’s commonly called an “All American Five.” This type of radio was built between about 1935 and 1960 by literally hundreds of US manufacturers. What distinguishes the All American Five is that it uses a set of five tubes whose filament voltages add up to about 120 volts. Since it has no power supply transformer it can be run on either 120 volts AC or DC (10 car batteries in series.)
The older version, made from the late 1930s through the 1940s used the 12SA7-12SK7-12SQ7-50L6-35Z5 tube lineup. The later version, made during the 1950s and into the early 1960s used the 12BE6-12BA6-12AV6-50C5-35W4 tube lineup. For survival use I recommend getting one of the later versions and keeping around a full set off spare tubes (especially the 50C5 and 35W4.) These radios are very sensitive and selective. At night they easily pick up stations up to 1,000 miles away.
“All American Five” radios often sell for around $20 – $30 on eBay. They make cheap insurance against EMP. Regards, – M.E.