What causes descending aircraft to make a noise like a giant blown bottle?
Short Answer:

The sound is caused by airflow across holes on the underside of the wings of certain aircraft.

Long Answer:

I too have noted the sound phenomenon that you describe. This video has a great example between 0:26-52 (link starts playback at 0:26 where the noise starts):

                
            

I will readily admit that this answer is mostly just a compilation of what I have learned researching this. Your question intrigued me and I've enjoyed learning about it!

As I discovered as I started researching this, many others are familiar with the noise as well. This article on Airliners.net had a lot of discussion about it, starting with a lot of interesting—but ultimately flawed—theories.

But, that thread led me to the answer to your question, which is: the sound is caused by the "circular opening used to equalise the pressure in wing fuel tanks", according to Euractiv.com

This article on AirportWatch further explains: 


  The Airbus 320 series of aircraft, [...] have been known for many years
  [...] to have a particularly irritating high pitched
  whine. This is caused by air rushing across the under-surface of the
  wing, where there are Fuel Over Pressure Protector (FOPP) cavities.
  This generates noise, in the same way as blowing air over the mouth of
  a bottle. Every A320 series aircraft emits a signature howling noise
  while approaching to land. It is heard most when the plane is
  travelling at around 160 knots, and the frequency is around 500-600Hz,
  which is close to peak sensitivity of the  human ear.


That being said, there is apparently a fix to that problem, as both the aforementioned links describe. As Euractiv.com explains, the fix is a vortex generator:


  a 5-cm triangular piece of aluminium sheet metal upstream of the two
  vents on each wing, in order to divert the air flow and stop the
  whistle. A decade of research went into the vortex generator, which
  stems from efforts to mask a similar whistle produced when air blows
  over the gun ports of warplanes.


This image shows both the FOPP hole, and the VG that softens the sound:

[Image Courtesy of Lufthansa]

Read the articles linked, interesting stuff therein!