Icicles are an iconic symbol of winter, reproduced in crystal, plastic, and lights as decorations on trees and houses. They are both beautiful and dangerous at the same time. Falling icicles have been used to take out the bad guy in books and film. Ralphie blamed an icicle falling from the roof for breaking his glasses in A Christmas Story when we all know he almost shot his eye out.
In reality icicles hanging from a gutter may be a sign of a much bigger problem especially during times of the daily temperature being around freezing. Inadequate insulation and poor airflow can cause escaping heat to collect in the attic which can melt the underlying snow closest to the top of the roof. The water runs down until it reaches the unprotected eaves and gutters where it refreezes before it can go down the spout. When enough ice accumulates it can actually prevent subsequent water from reaching the cooler section and refreezing. This water can then back up under shingles and start working its way into the house.
This can be mostly prevented with proper insulation and improved airflow. AIG offers this brochure to help you understand the potential danger and how to avoid it.