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Static Moon
"I've always wondered why the Moon's rotation matches that of its revolution around the Earth. Hard to believe it's coincidence. Is there something keeping this synchronization? Why do we always see only one side of the Moon?"
All pairs of gravitationally bound bodies tend to "sync" like this. However, it takes billions of years to become as apparent as the case of the Moon's sole face toward the Earth. In fact, most Moons in the solar system are sufficiently small compared to the planets they orbit that, over time, gravity has proven strong enough to lock the satellites' rotations to match their orbital periods.
The Moon is tidally locked to the Earth. When two rotating bodies orbit each other, they raise tides in each other. These tides cause mechanical friction. So tidal activity absorbs a lot of energy out of the rotational energy of the bodies. In other words, the energy in the form of rotational inertia is partially converted into tidal, geophysical changes in the bodies involved. The Moon's rotational inertia has been exhausted, converted into geophysical change in the Earth and Moon. The Moon, being much smaller than the Earth, long ago dissipated enough energy to lose rotation so that its tidal bulges are now always aligned with the gravitational pull of the Earth. The Earth still raises a "tide" in the Moon but it is in a balanced, steady state now and does not stretch the rock any more -- there's no more spin for the Moon to give up.
Since the Earth is still spinning relative to the Moon, the Earth is continuously and dynamically being affected by the gravitational pull of the Moon. The mechanical friction includes fluid flows around the Earth's surface as ocean tides, motion of the molten core within the Earth as well as the stretching of solid rock along the planet's crust. (For a sense of scale, note that maritime tides are recorded in meters while tides in the solid aspect of the Earth are recorded in centimeters.) This mechanical drag is a major reason for why the Earth's rotation is slowing. The day length is slowly lengthening, and has over geological time increased to 24 hours, up from 18 hours. Eventually, the Earth will no longer spin in relation to the Moon. Some time many billions of years into the future, the Earth will turn its same face to the Moon as well. (This isn't quite true; the Sun will likely "supernova," cancelling all bets, long before the Earth stops spinning.)
In comparison, the tidal effect on the Moon is static because the Moon no longer rotates in relation to the Earth. All these exerted forces are costs in energy. They have to come from somewhere. The Moon did have a much higher rotation rate long before anyone was living on the Earth to observe it, but the tidal forces slowed it down until it reached an equilibrium point, i.e., where keeping the same face toward the Earth was the point of least expended energy. Both will still rotate, both keeping the same face toward the opposite body.
As for why tides occur, the key operative phrase is "gravitational gradient." This impressive phrase simply means the pull on one side of a body (the near side) is slightly stronger than the pull on the far side. Here's a cute example to make the "gravitational gradient" more imaginable. During a full solar eclipse, the Sun, Earth and Moon align themselves such that the Moon is exactly between the Sun and the Earth (putting the Earth in the shadow of the Moon). If you happen to be on the side facing the Moon, you actually weigh less than if you were on the other side of the planet!
To further underscore the point that there are two tidal bulges, note that the gravitational gradient produces two high tides, one on the side being pulled more, and one one the side being pulled less (With low tides on the sides). This is the reason for why two high/low tidal cycles occur every day. The Moon also has two tidal bulges. As mentioned above, these are now static and aligned with the gravitational pull of the Earth.
Contrary to popular belief, however, the more massive side of the Moon does not point in the direction of the Earth! This might seem like utter nonsense at first. The Moon's Center of Gravity (CG) is slightly off-center, and in favor of the side of the Moon facing away from the Earth. When the Moon finally stopped rotating with respect to the Earth, the CG was in fact pointing the other way. How is this possibly a stable state? By itself, it's not. However, the gravitational gradient and the rotational inertia is more than sufficient to counteract this slight imbalance caused by the Moon's eccentric, opposite-facing CG. (Recall that the Moon does rotate in synchronization with its orbit around the Earth.) It's true that if the CG were toward the Earth-ward side, the tidal lock would be relatively more stable. The Moon's tidal lock is very stable, none the less.
"Wouldn't the kinetic energy of an asteroid hit cause the Moon to rotate with respect to the Earth?" The force of a sudden impact required to change the Moon's rotational inertia by even 1% would most likely cause the Moon to break apart. The rotational inertia of the Moon and the tidal lock with the Earth is sufficiently stable to resist all but a massive and destructive impact.
At present day, the Earth rotates once in 24 hours while the Moon orbits the Earth once in about 28 days. At stasis in the distant future, the Moon's orbital period won't be the present lunar 28 days, but something quite a bit longer. However, the angular momentum of the system must be conserved. So as the Moon's pull causes the Earth's rotation to slow, the Moon drifts farther outward into a longer period orbit. The system will stabilize where the two bodies are gravitationally locked. The total angular momentum of the pair will remain constant. (This is not quite accurate. The Sun also has a tidal effect on both Earth and Moon. This might be better said as, "The total angular momentum of all bodies involved will remain constant.")
"The Moon's orbital period will be longer and will be further out? Is this backward? Wouldn't the Moon's orbit *speed up* as the Earth's rotation slows down, and so be closer to the Earth?" No! This might seem intuitively contrary. Yes, the Earth is pulling the Moon, thereby transferring energy to the Moon's orbit. However, for a constant level of orbital energy:
there is more kinetic energy and less potential energy for a given mass in a smaller radius orbit (the mass orbits faster), and;
if a mass moves farther out, kinetic energy is traded for potential energy (the mass orbits more slowly).
The tricky part is this:
For a given mass, an orbit with higher energy has a larger radius.
With an elliptical orbit, the ratio of kinetic and potential energy will vary accordingly. The part that loses most folks is that if given more energy, the mass will go into a larger orbit, and will orbit more slowly. Most likely, the confusion results from using a mental model of a rotating object where the radius of the object is fixed (a steel wheel, for instance). The radius of an object held in orbit by gravity is perfectly able to adjust to the gravity of the system. So, by pulling the Moon, energy in the form of rotational inertia in the Earth is converted into orbital momentum of the Moon and so the Moon's orbital radius is increased.
"Does the Moon Wobble?" The Moon doesn't really wobble, but we do see more than 50% of the surface over time. The Moon's orbit is not a perfect circle, but is actually an ellipse. That means that when it is closer to the Earth it orbits a little faster; when it is farther out it orbits a little slower. The rate of rotation of the Moon itself is constant, though, so when the Moon moves at a different speed in its orbit, it is effectively changing the rotation rate relative to the Earth. Sometimes we see a little bit past one edge, and sometimes a little past the other (this is in the East-West direction). This effect is called "libration." As a result we're able to see roughly 50% of the lunar surface over time.
Repeating for emphasis, Libration occurs because the Moon's rotation has a constant angular speed, while the Moon's elliptical orbit has a varying angular speed. So it's faster when close to Earth, slower when farther away. Thus, the orbital angular velocity is sometimes slower than the rotational angular velocity and the Moon seems to rotate a little one way as seen from Earth. Then the orbital angular velocity increases again, catches up, and overtakes the rotational velocity, and the Moon seems to rotate the other way. And so on. Since the orbit of the Moon will never be circular due to perturbations by the Sun, libration is here to stay.
