It does spin.
It spins once per orbit, so that the same side is always facing the Earth. If it didn't spin at all, it would appear to make one revolution per
The reason why is called tidal locking. No large body has perfectly uniform density. There are off-center heavy bits here and there. Tidal forces are
exerted on these imperfections over time, and the result is that the body will eventually assume a tidally locked state.
There is more than one tidal locking mode. Mercury, for example, is resonantly locked to the Sun at a 3:2 ratio.
Go Google for "tidal locking", there's lots of sites with drawings and lengthy explanations.
[edit on 30-9-2007 by Tom Bedlam]