|MadSci Network: Astronomy|
You're right, the chance that our Moon's rotation rate should exactly equal its orbital period are too low for this to have occurred by accident. What has happened is that the Moon probably span much more rapidly in the past but has been locked with one face towards the Earth by a process known as tidal friction.
The Moon's gravity tends to deform the Earth's surface very slightly away from a spherical shape, by elongating it along a line joining the centres of the two. This leads to tides in the ocean, as well as slight deformations of the crust of the Earth. Similarly, the Earth's gravity raises tides in the surface of the moon, distorting its shape along the line joining them both.
If the Moon were spinning so that it presented a different face to the Earth every night, the changing tides in the lunar surface would dissipate energy from the Moon's rotation, as different parts of the surface rose and fell under the influence of the Earth's gravity. Over time, the Moon would slow down and settle into its most stable configuration, with one face constantly toward the Earth and the tidal distortion of the surface constant and unchanging. In turn, the Moon's tides acting on the Earth also slow the Earth down, and the most stable configuration for the Earth-Moon system is for both to spin so slowly that they present the same face to each other.
The Earth-Moon system hasn't quite settled into this state (although the Earth is still slowing down, at a rate of about 16 seconds per million years, I think) but the Moon's orbit has been locked into its most stable state, which is why the same side of the Moon always faces the Earth.
There's a little more information about this this web page: Why Doesn't the Moon Rotate?
Try the links in the MadSci Library for more information on Astronomy.