I heard about a medical device called an external fixator (sometimes
called an Ilizarov device) that allows doctors to change the size and
shape of extremities (usually arms, legs, or fingers) over time by
applying continuous low-level
tension.  I also recall having seen tribal body modifications that
use the same principle.  My question is this: if this works on other
body parts, can it, in principle, work on the penis?  If not, why not?
 I see that there are stretching devices for sale, but I have always
dismissed them.  However, I am wondering why they wouldn't
work if this technique in fact works on other tissue.

The shapes of other extremities can - through a long procedure - be
changed because the bones inside them are slowly deformed. A penis,
however, does not contain a bone...

Scriptor

Even if you could successfully stretch your penis and have it stay
that way, you'd gain length at the expense of width. If your aim is to
please a woman, you might want to consider that most women wouldn't
consider a long, skinny penis to be an improvement over a
normally-contoured one. It might have problems with bending, too.

I am aware that the penis does not contain a bone :)  But when
extending other body parts the surrounding tissue must grow to extend
as well, no?  Also, people who stretch their earlobes or lips are not
relying on bone growth.  Is erectile tissue unique in it's inability
to grow under tension?

With regard to length over width: I imagine that if tissue can be
enlarged by extended tension, that a uniform vacuum such as those
pumps already marketed could increase both length and width.

I guess my questions are, most succinctly:

1. Does body tissue really grow (i.e. cell division, etc) in response to tension?
2. Would the penis somehow be exempt from this effect?

And just to preempt posts about my personal penis size concerns, I'll
just say I'm of average size and married with a healthy sex life. 
This isn't an area of great concern for me personally, I'm just
curious about the biology of it.

Thanks for your comments!

The Ilizarov external fixator is designed to fixate healing bones.  It
can stretch a broken bone by allowing for gradual extension of the
external device.  The bone, which is not yet healed, is stretched
apart as it tries to heal.  This is done very slowly and the non-bone
(soft) tissues are stretched.  When the limb reaches the desired
length the extension is stopped and the bone is allowed to form a
typical bone "callous" and finally heal.

Penile lengthening is generally considered to be a hoax.  There are
many creams and devices on the market which are largely ineffective. 
There are some surgical techniques that have been tried.  Please see
the links below.  A traction device such as suggested in the question
is unlikely to be effective because of the way in which a penile
erection is achieved.  Under normal circumstances the arterial inflow
into the penis is increased between 20-40 times normal.  This is a
much greater increase in flow than what is seen anywhere else in the
body.

Under the influence of chemical mediators the muscular corpus
cavernosum (two spongy chambers on the top surface of the penis) and
the corpus spongiosum (the chamber on the underside of the penis) are
caused to relax.  The caveties within the three chambers enlarge and
blood rushes in.  When the chambers fill (inflate actually) they will
eventually meet resistance when they come up against the tunical
albuginea.  The tunica is a inflexible tube around the three spongy
chambers.  It is this inflation within the tight and restrictive
tunica that gives the penis rigidity.

At this point the large increase in blood flow into the penis returns
to normal.  The reason the erection does not go away at this point is
because the venous outflow from the spongy chambers is cut off -
squished between the outside of the corpus cavernosum and the tunica
albuginea.

Now - how is all of this relevant to the question?  If the tunical
albuginea was flexible and stretchable there would be no erections. 
The outflow of blood from the corpus cavernosum would not be cut off
and there would be a "venous leak" or a "failure of venous occlusion"
as it is also known.  Therefore, the tunical albuginea is too
inflexible for significant enlargement through non-surgical means. 
Try some of the links below.  ms

http://images.google.ca/imgres?imgurl=www.astrazeneca.no/images/medica/ur_99023_impotens.jpg&imgrefurl=http://www.astrazeneca.no/bibliotek/azmedica/urologi/impotens/ur_99023_impotens.html&h=630&w=599&sz=45&tbnid=6hzFDWrLhz8J:&tbnh=133&tbnw=127&prev=/images%3Fq%3Dtunica%2Balbuginea%26hl%3Den%26lr%3D%26ie%3DUTF-8%26oe%3DUTF-8%26sa%3DN

http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=12152118&dopt=Abstract&itool=iconabstr

http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=11119096&dopt=Abstract&itool=iconabstr

http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=10643519&dopt=Abstract&itool=iconabstr

http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=10081856&dopt=Abstract&itool=iconabstr

A Word of warning.  It is rare that the answer to a
less-than-satisfactory-sex-life is a longer penis.  There are much
better ways to please her...but that is another question.  ms