Gutters can be a source of roof leaks. This is because clogged gutters can cause rainwater to backup and go under your shingles into your roof.
Therefore, it is important to keep your gutters clear because not doing so leads to leaks and other roof problems such as moss buildup on shingles and shingle deterioration.
Keeping your gutters clear is a part of regular maintenance of your roof. Not doing so can void the manufacturer's warranty of your roofing material because in the fine print it says that regular maintenance is a requirement.
Gutter cleaning in the late fall should be included with a regular roof inspection to ensure your roof stays in tip-top shape.