Most are easy to remove — with the caveat to work safely. That means only on walkable (low-slope) roofs in good weather and only if you are comfortable being up there. Steeper slopes that require scaffolding and safety rigging are for pros.
Roof debris. Leaves, pine needles and other debris collect in the trouble spots. If you're not sure where they are, the piles will show you. One chronic headache is the high side of chimneys. These used to be fitted with special flashing called a cricket — a large metal piece with a raised ridge down the middle that pushed drainage to the sides. Because it's expensive to fabricate and tedious to install, many chimneys have flat flashing against the chimney instead. There, and at any blockage, debris piles can slow drainage and foster ice dams in winter. Repairing or replacing flashing, worn shingles and other defects may be necessary. But the first step is to sweep the roof clear of debris.
Flashing. Loose flashing can also block drainage, and worse yet act as a funnel that directs rain through the roof. Around chimneys, for instance, the top edge of flashing should be mortared in place between courses of masonry. But flashing applied during many re-roofing jobs is often pasted in place with roof cement, which works loose and creates a funnel.
Gutters. Even one twig stuck in the wrong place can cause a pileup and bring the flow to a halt. To find it, scoop debris from the gutter into plastic bags instead of trying to wash it through the downspout where the clog may reform. Then test the system by flooding the gutter using a garden hose to see if it drains freely. There are many types of gutter guards designed to prevent blockages, such as wire baskets and gutter screens. The idea is that wet debris dries out on top of them and blows away.
Downspouts. When gutters won't drain freely after cleaning it's because of a blockage farther down the line at one of two usual suspects. First is the offset fitting, an S-shaped piece that channels water from the gutter back to a downspout mounted against the house. Its shape is a built-in bottleneck that may not clear even after flushing with a garden hose. Take the fitting apart for cleaning.
Second is the end of the system where downspouts empty into underground pipes that carry water away from the foundation. (Open-end spouts rarely clog but dump water against the foundation.) Clogs in underground pipes can be detected by scoping — sending a snake with a minicam down the line — and then cleared with a cutting snake if the pipes are intact.
Yard drainage. The best drainage layout releases water from downspouts where it flows away from the building. A concentrated flow there (or constant dripping from the eaves) erodes a gully that will trap water and foster foundation leaks. Eliminating that problem is easy where ground naturally slopes away from the house. A short elbow on the downspout and a splash block to prevent erosion will do.
It gets more complicated where ground slopes toward the house. You have to take the deluge from a downspout around the corner to a downhill release point. And to keep the water moving — either aboveground with downspout extensions or underground with plastic pipe — the extended drain system should have a slope of at least 1/8-inch per linear foot.