I've long suspected that it was no coincidence that the Moon always keeps the same face towards the Earth, but I never actually knew why until yesterday.
There is indeed a negative feedback loop that tends to synchronize the Moon's rotation with its orbit. This phenomenon is called tidal locking.
The Earth exerts a tidal force on the Moon, elongating it in the direction of the Earth-Moon axis (and compressing it in the perpendicular directions). However, since the Moon resists being deformed to some degree (don't we all?), if it rotates faster or slower than its orbital angular velocity, the axis of elongation can run ahead of, or behind, the Earth-Moon axis. In either of these cases, the Earth's gravity provides torque on the moon to slow down or speed up its rotation, respectively. Thus the Moon tends to keep the same face towards the Earth.
The things you learn every day!