I noticed several years ago that when I took analgesics fairly regularly,
(motrin at the time), I seemed to get a lot of migraines.  But had
forgotten about that until I started reading some of the posts here.
I generally don't take NSAIDS or Tylenol for headaches, because I've
found them to be ineffective.  However, I have two other pain sources
that force me to take NSAIDS (currently Naprosyn).  First, is some
pelvic pain that I get at the beginning of my period, and then much
worse at midcycle.  I have had surgery for endometriosis in the past
(~12 years ago), so the Drs. tell me that my pain is probably due
to the endometriosis coming back.  I've tried Synarel, it reduced
the pain while I took it (3 mos), but the pain returned immediately
after I stopped.  Three doctors have suggested hysterectomy as the
only "real solution" to my problem.  Although I don't expect to have
any more children, I don't like the idea of having my uterus and
one remaining ovary removed (the first ovary was removed when I had
the surgery for endometriosis).  One of the Drs that suggested
I get a hysterectomy is an expert in laser surgery, but perhaps thinks
that type of procedure is only worthwhile on women who still plan
to have children.  So basically all I'm left with is toughing out
the pain.  This would be impossible without Naprosyn (or something
similar - but not aspirin, that doesn't work, and Motrin gave me
horrible gastritis a few years ago, so I'm through with it).  In
fact, Naprosyn works very well at eliminating the pain if I take
it regularly as I did when I had severe back pain (and pain in both 
legs) as I'll discuss in a moment.  Generally though, I wait until
I have the pain before I take the Naprosyn, but then it takes
several hours for it reduce the pain (it's actually quite effective
at reducing the pain, it just takes quite a while).  In the meantime
I'm frequently in severe pain.

The other pain source I have is chronic lower back pain resulting in
bilateral radiculopathy.  I've had MRIs, Xrays, CT scan, and EMGs
(I've had 2 of them, and don't intend to ever do that again) with
nerve conduction tests.  The tests have not been conclusive as to
what is causing my back and leg pain.  The MRI reports both say I have
several bulging, degeneratig disks, and from the Xrays (and MRI, I think)
it is apparent that I have arthritis.  The reading on the CT scan
was that there are two herniations (L3-L4, and L4-L5), but others
hav looked at the films and concluded that there are no herniations.
The second EMG and nerve conduction studies shows significant denervation
compared to the first EMG.  Oh yeah, I had some other horrible test,
called something like Somatic Evoked Response which showed that the
"internal nerves" are working fine.   Anyway, the bottom line is that
I sometimes have severe pain in both legs and back pain.  The back pain
is there all the time, but I can live with it.  When the leg pain is there,
I need some analgesic/anti-inflammatory medication to reduce the pain
to a level where I can work.  So I took Naprosyn regulary for 6-9
months (every time I tried to stop the leg pain got worse, so I'd 
always resume).  Since last November I have taken it much less frequently,
and primarily for the pelvic pain.  I have been going to physical
therapy for the last 8 months (2-3 times a week).  After the first month
or so, my therapist put me on pelvic traction (she had tried it earlier,
but it had caused a lot of pain in my back, this time she tried it at
a lower weight).  After a month or two, the pain in my legs began going
away (but the traction aways caused discomfort in my lower back, which
could be reduced with ultrasound and massage).  So now, I don't have
nearly as much pain in my legs, in fact my therapist took me off
traction about 2 weeks ago.

Getting back to my original reason for this post...  Even if I can avoid
taking analgesic for headaches, I really can't avoid them entirely because
I have other pain sources, that "force" me to use them (Oh, I forgot
to mention that it has been suggested to me that I have back surgery,
but I'm avoiding that too).  I find the migraines difficult to deal with,
occassionally I have to take off work, but usually I can work, but at
a reduced capacity (I'm a systems engineer and do a lot of reading
and writing).  When the pelvic pain is bad, I can't concentrate much,
I usually end up jumping out of my chair every few minutes, because
the pain is so bothersome.  When the pain in my back is bad, it can
cause severe burning in both legs, shooting pains in my legs, electric
shock type of pain in my feet and toes, and basically when it gets bad
I can't really sit at all.  Then I end up spending most of my time home
and in bed.  So even if the analgesics contribute to the migraines, the
migraines are more tolerable than the other pain sources.  I get a lot
of migraines, an average of 3 to 4 a month, which last 1-3 days.
I've taken cafergot (the first time the caffiene really got to me so
I reduced the dosage), but I don't like the side effects (if I take
more than two I get diahrea).  If I get a very bad headache, I will
eventually take the cafergot.  My neurologist wasn't very helpful when
I told him my problems with cafergot, he said that when sumatriptan
becomes available, I should try that.  I've tried several other medications
(fiornal, midrin, fiornal with codeine, tegretol, and inderal) but
they either didn't work, or I couldn't tolerate them.  So what can I do?
My doctor's seem to be satisfied with me just trying to tolerate the
pain, which I agree with most of the time, but not when I have a lot of
pain.  I've had some bad experiences with surgery (my heart stopped
once from the anesthesia - I was told that it was likely the
succinylcholine), and I've already had surgery several times.

Anyway, the point of what I'm saying is that even if analgesics can contribute
to migraines, some people NEED to take them to tolerate other pain.