An all-perils homeowners insurance policy does not usually provide coverage for an actual broken pipe. However, the water damage that the broken pipe causes would be covered under most circumstances.
Most insurance companies would consider a home's plumbing to be under normal homeowner maintenance. The property owner is responsible for repairing or replacing the broken pipe. Leaky pipes are different from broken pipes that could potentially flood the entire home. This type of flood is covered under an all-perils policy. A flood from rising water would require separate flood insurance coverage.
If you live in a northern climate and your broken pipe is a result of freezing due to a lack of heat in the home, an insurance company could cite your negligence and deny your claim. Broken pipes must happen suddenly and by accident and shouldn't have been easily preventable. If you ignore a leaking pipe, and it subsequently bursts, the insurance company can see evidence of a long-term leak and deny the claim.
After a pipe bursts, homeowners insurance covers damage occurring to the carpet, drywall, paint and so on. Any service needed to clean up the water, dry out the home and possibly prevent mold would also be included in this coverage.
Have your plumbing inspected by a licensed professional on a regular basis. Different portions of your home's plumbing will have various life spans. Replace pipes that are beyond their intended life cycle. In northern climates, be sure to leave your home's heat on, even if it is set to low, during the winter, especially if you are leaving for an extended period of time. Every home, regardless of climate, should have a water shutoff valve. Know where this valve is located, and make sure it is operable in case you need to turn the water off quickly.