I have a living room where I will be hanging drywall over the old
plaster walls.  There is some decorative trim or "molding" around the
ceiling, and I would like to remove it, hang the drywall, and put it
back up over the drywall afterwards (trimming the ends slightly to
accomodate the thickness of the drywall board).

My question is how to remove the molding without damaging it, so it
can be replaced later.

The walls are old plaster that can be damaged slightly, as we will
cover them.  The boards are nailed to the wall, every few feet.  The
ends of the board are mitre-cut at 45-degrees.  Each piece of molding
is one long wooden board, either 13 feet or 15 feet long, matching the
room dimension.  The wood is probably at least 50 years old.

Here is an ASCII art diagram of a corner, looking down from above
(through the ceiling):

          wall
 ________________
.\         |
|\\        |  molding board
| \\_______|_____
|  \       _
|  |      nail
|  |
|---| nail    interior of room
|  |

I don't think I can pry out the nails from the face of the wood
without damaging the face (the visible part).  The obvious thing to
try is to pry the board with the nails out of the wall. The problem
then is that the ends of the trim boards are held in place by the
adjoining board, since their ends are cut at a 45-degree angle.  How
should I proceed in removing them?  Should I just use a hacksaw to cut the
nails from behind, since I can slip something thin in between the
molding and the wall?  Or is there another way?  Can the molding be
cut in half so that the seam can be hidden later?  Is there a way to
convince the nails to come out of the wood from the front?

I have searched Google for "removing old molding" and "removing old
crown molding" and "removing trim" but I get pages that either talk
about *installing* new molding or pages that talk about removing
baseboard trim (e.g. houseinprogress.net) which is easier because the
boards are simply fastened to the wall, and are not "pinned" in place
by other boards.

Generally, using a pry bar to coax the molding away from the wall is
enough. Pry a bit, move to the side, pry a bit, move to the other
side, etc, and when you go back you can use small wedge blocks as
spacers. You'll get some flex in the strip and be able to "snap" it
out of the hold that the two perpendicular pieces have on it. Once one
is out, the remaining ones aren't held in.

If the molding is very tight, you can start with a putty knife. Get it
in and work it a bit, maybe using a wedge for leverage.

If you read the installing molding pages, you will see that there is
supposed to be a little bit of "spring" in the crown molding when it
is installed, to compensate for shrinkage.  ["I was in the pool!"]

You may come across a molding strip that is actually two pieces.
Properly done, this involves a miter somewhere in the run rather than
just butting the ends (I used an angle of 70 degrees when I had to do
this). If you have one of these, you might be able to find it before
disassembly to ease things.

Some molding isn't mitred in the corners, though-- it's coped.

Good luck on your project!

One approach I've used when removing molding I wished to reuse is to
drive the nails right through the molding with a thin punch. You are
left with extra holes to fill when you reinstall the molding but that
isn't too onerous, and for me it's faster than the pry method.

In the corner use a razor blade to score the line were the two pieces
of molding meet. As the paint can adhere the two pieces together. then
wedge a putty knife between the two pieces. this will help the pieces
slide along each other without chipping. As in previous comments there
may be more that one piece of molding along a given wall and it may be
easier to start at one of these joints. The scoring with a razor blade
however holds true at any meeting of the trim.
There is a nice post to a forum here:
http://www.bobvila.com/wwwboard/messages/118992.html
and a tip here:
http://www.bobvila.com/TipLibrary/Task/Building/0432-Removing_Old_Woodwork.html