I have a phone with service from Cingular;  about a year ago I changed
my number to the 650 (Palo Alto) Area Code.  Since then, roughly every
two weeks or so, I receive a call from a 650 number;  if I answer, I
hear silence (or sometimes faint static, with echo), and the other
party will end the call within a minute.  If I don't answer, the call
may or may not leave an empty (with static) message on my voicemail.

So the interesting thing is, on a day when I get these calls, I'll
usually get several of them, maybe ten minutes apart, within an hour,
all from the same number.  But between days (usually weeks), the
number will be completely different from previous 'silent' numbers.

Finally, if I attempt to call back, random citizens of Palo Alto
(sometimes businesses, sometimes households) will answer, baffled at my
allegation of having received several calls from their number.

What's happening?!  I'm fully convinced that the people identified by
Caller ID are NOT the ones actually calling me -- and while I'm aware
that methods for spoofing Caller ID exist and are fairly simple to
implement, I can't imagine what the motive might be, and the
particular pattern of calls boggles my mind.  Any help solving this
mystery would be greatly appreciated!!

Are the people you call businesses or individuals generally?

Some electronic devices and machines (such as drink dispensers, some
satellite and cable boxes) are programmed to dial a certain number
when stock is running low or they need attention. If your number is
similar to the local one, you may receive a lot of wrong numbers.
Obviously the machine would repeat the call if it didn't get the
correct answering code.

I'm not an expert in these things, but I assume that a second number
would be programmed into the machine in the event that yours did not
work, and that future calls would be diverted to this number.

Then again, I may be barking up the wrong tree completely...

Interesting idea!  It turns out that the majority (say 3/4ths) of my
callbacks have landed individuals, and only a small portion
businesses.  But who knows -- some folks in Palo Alto have pretty
outrageous houses -- next time I get a random call I'll ask them if
they have a soda machine. :)

Thanks for your comment!