The chimney of your home is one of the most important features of the building. Even though the chimney is not a structural component, it is one area prone to problems and often overlooked. As a home inspector, I see two primary problem areas with chimneys.
The first problem is the chimney cap, specifically concrete caps that fail at a significant rate, even on newly constructed homes. The cap is subjected to extreme weather conditions and when water begins to penetrate and freezes, the concrete starts to fail and crack. Once the water gets between the block / brick and the flue liner, water pressure creates a condition known as efflorescence, which can result in deterioration of the mortar joints. At this point the cap needs to be pointed up to prevent further damage. Hydraulic cements, while costly are excellent to use to waterproof these areas. You can also use Portland cement, which is available. Using either of these products will greatly increase the life of your chimney.
The second problem can be the lack of a water saddle or cricket. The cricket is basically a small gable roof installed behind the chimney, at the main house roof slope. This cricket will divert water around the chimney and will not allow snow and ice to build up behind this area. This is even more of a serious problem when the chimney is beside a second level of an adjoining building. Rot and deterioration can result from the water and snow building up along side the wall and thus working it's way underneath the siding. Ice dams can also occur under the shingles, causing nail-popping and possibly the sheathing to rot.
There are many homes even new construction without crickets being installed. The installation of a cricket should add minimal expense to the cost of a new home. If you live in an older home, these two areas should be check and remedied to prevent costly future repair bills. If you are building a new home you should be sure and discuss these areas with your building contractor.