Well the first and most obvious and apparent danger is your safety. Nobody wants a part of their roof to cave in and fall on their head. Mold is known to grow in wet and damp places. If their is leakage inside your drywall then you are sure to have mold. This is extremely dangerous for your health and immune system. There is always a chance of getting electrocuted with water dripping around everywhere. It is also possible that your whole electrical system can short out, which can be costly to fix.
To prevent roof leaks it is important to know some causes. Poor roof construction happens often due to the bad economy and contractors cutting corners. Sometimes contractors have to build in bad weather to meet deadlines and moisture gets trapped in roofing system which can contribute to early roof failure. Normal aging happens due to the beating roofs get from weather. Settling happens with every building. This will cause enough stress eventually to cause a leak. Mechanical damage is also a strong contributor. Having heavy stuff on your roof such as air conditioning units, TV satellites, signs and elevator housings can put extra weight on your roof and require more services (foot traffic) on your roof.
It is best to have a professional come out to check your roof every couple years to ensure the safety of you and your family.