Foundation Damage. Water is a home's worst enemy. Your gutter's job is to direct water away from your house, so that your foundation and property stays dry. Dirty gutters will clog up your system and will often cause water to pour over the edge. If excess water builds up around your house, over time it could lead to cracks and mold in your foundation, and sometimes even foundation collapse. Yikes!
Water backup and Roof Damming. When debris builds up in your gutters and clogs the system, your gutters will overfill and begin spilling over. This excess water can cause damage to your roofs fascia boards, which are made of wood. These can rot pretty quickly, especially if they're constantly saturated with water during rainy seasons. Clogged drains can also cause water to pool up and cause even further damage to your roof, especially during winter months when ice build up thaws and freezes constantly.
Tips. Using a pressure washer can really help thoroughly clean hard to get to areas and reduce the time you spend actually on the ladder with the hose in hand. If you can't find any affordable options at a local hardware store, then you can probably rent a pressure washer for a day from somewhere nearby you. If not, then the traditional hose and gloves trick does the job great too.
Don't forget to seal the edges and connections of your gutters with gutter sealant. Doing this step will help stop leaks and prevent them from forming in the future.