In fact the Moon *does* rotate: It rotates exactly once for every
orbit it makes about the Earth.  The fact that the Moon is rotating
may seem counterintuitive: If it's always facing towards us, how can
it be rotating at all?  To see how this works, put two coins on a
table, a large one to represent the Earth, and a small one to
represent the Moon.  Choose a particular place on the edge of the
"Moon" as a reference point.  Now, move the Moon around the Earth in a
circle, but be careful to always keep the spot you picked pointed at
the Earth (this is analogous to the Moon always keeping the same face
pointed at the Earth).  You should notice that as you do this, you
have to slowly rotate the Moon as it circles the Earth.  By the time
the Moon coin goes once around the Earth coin, you should have had to
rotate the Moon exactly once.

This exact equality between the Moon's rotation period and orbital
period is sometimes seen as a fantastic coincidence, but, in fact,
there is a physical process which slowly changes the rotation period
until it matches the orbital period.  See the next entry.