Is an air-to-air rescue as shown at the end of the movie "Air Force
One" an actual possibility? Has it ever been done in an actual rescue
situation? The answer should point to references on air-to-air rescue
where a cable is connected between the aircraft and people are removed
from the stricken aircraft.

I only located a DoD briefing that indicates such rescues are
unrealistic:
http://www.defenselink.mil/news/Oct1999/t10261999_t1026asd.html
Q: People who watch, I don't know, popular movie culture have perhaps
an overly optimistic idea of what it is the military can accomplish in
terms of some sort of air to air rescue or something like that?

Mr. Bacon: Well, I don't think many people would believe that to be
possible. I think what people should take away from this is that the
FAA as the supervising agency, working with military support,
performed competently, calmly, quickly and brilliantly in the face of
a very potentially risky and unknown, scary situation. And I think
from the very beginning when they discovered that they couldn't make
radio contact with this plane, what you saw was a very rational and
competent approach to dealing with the problem. And part of a
rational, competent approach is not overreacting. And I don't think
there was overreaction here. I think that they were able to calculate
where the plane was going. They made reasonable judgments, and those
judgments turned out to be correct.
secret901

fyi:  A special Air Force unit based in Hawaii, the 6593rd Test
Squadron
flew modified C-119 and C-130 aircraft.  Good place to start
researching.  Good luck.

It is TREMENDOUSLY unrealistic.  Most people don't realize the effect
the 150+ mph "wind" would have on the human bodies as they attempted
to travel from one aircraft to the other.  Think of a little flag on
the antenna of a car going highway speed.  See it whipping?  Now put
one of those little green plastic army men on the end of the flag. 
See how he's whipping?  How long could you survive that?  Real life
example:  If a paratrooper gets hung up on the way out the door of a
C-130, the turbulence will beat him senseless in just a few seconds. 
It'll kill him in a few minutes.  The wind forces are so strong, in
fact that it requires a special winch in the plane for just such an
emergency.  It's called a Static Line Retriever.  The aircrew has a
few minutes to either get the trooper winched back in or to cut him
loose and hope he's still conscious enough to pull his own backup rip
cord... but tethered there to that aircraft, he's a dead man for sure.

So can you take a cable, tether a couple planes together, and transfer
civilians across it?  Not a chance.  Has it ever been done for real? 
Nope.

Bob

Thanks for your response. As the poster of the question, I would
consider your comment an answer, and the question to be closed. You
have a very good point. I knew it all looked impossible, but I
couldn't put my finger on why. You did. Thanks.