The root of the problem is the nature of water itself. Almost every material in the universe shrinks or contracts in size as its temperature is lowered. Water contracts in similar manner as the temperature drops, but only to 32° degrees Fahrenheit. Below that temperature, water has a unique property: it actually begins expanding. Imagine a sealed pipe and the water contract down to 32° degrees with no problem. However, at 32° degrees and below, the pipe is still shrinking in size while the water starts growing in size. With faucets closed, the pipes cannot release the increasing pressure of the frozen water. Intense pressure develops and increases until the pipe splits or tears to release the pressure. Both plastic (PVC) pipes and copper pipes may burst. The water is still frozen, however, and will not begin dripping, leaking, or spraying until it thaws back into liquid. When the thawing does occur, the water escapes the pipe and begins damaging from water.
The best approach to the whole threat of frozen damage would be prevention. The pipes most susceptible to freezing are usually those that are near outer walls, in crawl spaces, or in the attic. All of these pipes should be properly insulated and even wrapped with approved heat tape where necessary. Outside leaks of air should be sealed. Garden hoses should be disconnected and where possible, pipes leading to outside pipes should be shut off and drained. Open doors to interior cabinets containing water pipes in order to circulate warm air inside them. As a hard freeze approaches, open both hot and cold faucets to a trickle to help prevent the water from freezing. (The water department wont give you a break for the increased water usage, but you may end up saving thousands of dollars in potential damage claims.)