Keep tree limbs from touching the roof. They can damage the shingles, and the leaves will clog your gutters.
See if there are black streaks on the roof. If there are, it means that mold, algae or fungus is growing on the shingles. If it isn't removed, it will eat away the shingles and lead to leaks. The north side of your roof is especially vulnerable.
Make sure the attic space is well ventilated to keep moisture down and prevent the growth of moss.
Wash your roof with a garden hose, taking care to do so from the top down. Directing water up onto the roof from the ground will result in water getting between the shingles. If a simple hosing down doesn't get the roof clean, try using a long-handled brush to gently scrub the shingles.
Check for missing or damaged shingles, especially after windstorms. If they are asphalt shingles, you can do the work to replace them yourself. Otherwise, have a professional replace them as soon as possible before a leak occurs. Also check for bent flashing.
Keep your gutters clear of debris and remove snow and ice promptly. Snow on the roof can cause ice dams, preventing water from leaving the roof promptly.
Check your interior walls, ceilings, exterior vents and chimneys for signs of water leaks. If you find evidence of a leak, figure out where on the roof the leak is originating and fix the problem by replacing the shingle, repairing the flashing or applying a sealant.