If gutters are clogged, rain water won't be directed away from the home. Water can build up near the roof or foundation, and eventually begin leaking into the home. This can cause mold, mildew, and extensive water damage. It can also make the home more inviting to termites and other pests.
Over time, water dripping near a foundation or onto sidewalks can cause the cement or brick to break down. If there is a garden, bushes or other landscaping below the gutters, these can become damaged as well.
If the gutters are clogged over the winter and are located in a cold climate, ice dams can form in the gutters. These are very heavy and can cause damage to the roof, the gutters and potentially the side of the home.