For radiolocation work, high-impedance headphones are really the only way to go!  The very low audio current in the cord and earpieces helps reduce feedback problems between the receiver operator and the nearby loop antenna. There is also less audio current drawn from the battery, which reduces internal feedback problems inside the receiver. My DQ receiver uses an LM-386 audio amplifier, but could use a simple op-amp with high-impedance phones.  32 Ohm stereo phones are available almost for free these days, but they are only 16 Ohms when the jack is wired for mono.  Also, most have an "open" design that does not block outside noise.  16 Ohms is marginal for the DQ receiver.  The 8 Ohm "hi-fi" phones are even worse.
         The gold standard is crystal headphones, with high impedance and no coil winding at all, but they are hard to find these days. See below for a home made alternative!  For several years I have been using some old  Telex monaural "language lab" phones (pictured below) that I bought at a flea market.  They are rugged, block outside noise, stay on your head, and cause feedback only when placed right on the loop antenna.  The high frequency response is limited to 12,000 Hz, which reduces electronic "hiss".  I was surprised to find out that they are still available new at a reasonable price!  There are 3 versions, all of which look the same.  The first is Telex model 610-41, which is a 600 Ohm mono headset with 1/4" (6.35mm) plug.  Next is the model 610-44, which is 600 Ohm mono with a standard 1/8" (3.5mm) mono plug.  Last, and to be avoided at all cost, is the model 610-44S, which is the 600 Ohm STEREO version!
NOTE DEC 2011:
    These headphones are no longer being manufactured, but are still being sold on Ebay.