What radio frequency bands are associated with the long wire antennas, why do some aircraft have them and others don't?
Depending on the aircraft you could be looking at one of a few things. 



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On some older aircraft it may be the communications antenna for older style radios (pre UHF/VHF days). Most of these radios have been phased out for some time but you will see it in pictures. 

The more common thing you are seeing (based on your top of the fuselage to front of the tail description), as it is still in place on many small GA planes and any bigger planes that have not had the unit removed is the ADF Sense antenna. This antenna helps to deal with the directional ambiguity problem in an ADF unit. Basically the loop antenna is capable of knowing where the station is but only on a 0-180 degree plane. It does not know if it is in front or behind the antenna. The sense antenna allows it to solve this ambiguity. These units operate in the 190-535kHz range. For what its worth the FAA is pulling a lot of ADF's and their associated approaches as GPS takes over but they seem to still be common elsewhere in the world.   

Here is one, 


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  Why do some aircraft have them and others don't?


Since it seems like we have settled on the ADF sense antenna as the one in question it boils down to weather or not your airplane has an operational ADF installed. ADF's are still popular elsewhere in the world but here in the US much of the ADF system is being pulled as it was in part replaced by the VOR system much of which is to an extent being supplanted by GPS today. Since a large chunk of the GA fleet and to an extent the commercial fleet has airframes dating from the ADF days many of the planes still have the systems installed. Depending on where you are located, if you routinely fly one of the remaining ADF approaches or otherwise use an ADF regularly you may elect to keep it in your aircraft. I can tell you that none of the aircraft I trained in had operational ADF units although two of them had units with antennas but were non operational and simply had yet to be removed.