The immediate disadvantage of a tidally locked planet is obvious. One side of the planet cooks while the other freezes. Water on one side is vapor, and on the other side is ice. If there is any appreciable amount of life on the surface of the planet, it has to be in the twilight strip of land between the two halves.
But it's not as simple as getting the temperature right. If our atmosphere permanently lost the heat of the sun, it would first turn into a denser gas, then condense into a liquid, and then further condense into solid ice. Meanwhile, air that is constantly exposed to light — or that is heated by a ground that is constantly exposed to light — will heat up and expand.
Although it's doubtful that the atmosphere on the dark side of the planet would get to solid form, it would certainly keep condensing and leaving a vacuum to suck in the expanding hot air from the other side. This might make for circulation of atmosphere that would make the planet livable, but it would also lead to hellish storms, as the atmosphere from the light and dark side of the planet essentially switched sides continually.
And those winds may bring some very, very nasty things with them. Even geologists foresee major problems with tidally locked planets. Rock and soil erodes differently when it's exposed to different levels of light. The cool side of the planet is preserved fairly well, but the lit side of the planet is stripped of its oceans and made to face burning sun and scrubbing wind every day. It will erode faster, and rocks that might have turned to terrestrial sand in a climate with night and day may be vaporized, picked up by the wind, or dissolved in water vapor to go airborne. Life, if it manages to struggle along on such a planet, will either be underground or very, very hardy.
So why are some planets and moons tidally locked while others are not? All planets bulge towards their stars, and all of them have their orbit slightly out of sync with their rotation. The mechanics of how it happens are the same in every case — but whether tidal locking actually happens depends on things like orbit distance, the mass of both bodies, and the malleability of the orbiting object.
Generally, closer objects are more likely to experience tidal locking. Far-away objects are less likely to experience dramatic differences in gravity between their two sides, resulting in smaller bulges, and the bulges themselves will feel less of a pull. For many stars, the habitable zone — the ring of space within which planets are able to sustain life — overlaps partially with a zone that makes planets likely to be tidally locked to their star, making them significantly less habitable.
Nervous scientists have speculated that the Earth might eventually be a tidally locked planet, but it appears that such a fate is not in store for us. At least not with the sun. The Moon, which we've already ensnared, might turn the tables on us. The Earth's rotation actually gets slowed down by the Moon a little bit each year.
There are many factors involved in calculating how slow we'll get. For example, we have to consider whether the Earth will continue slowing at a steady rate, the fact that the Moon drifts a little away from us each year, and the question of whether or not the sun will eventually swallow both the Moon and the Earth when it goes red giant. But someday, the Earth might be tidally locked to the Moon. In that case, only half of the Earth will ever see the Moon. So think of how lucky you are to see it nearly every night, even though because it's tidally locked you can only see half of it.