There are a couple of ways to minimize ice dam damage or to avoid the ice damming problem altogether.
1.This method can only be implemented when you install a new roof. Insist that your roofing contractor install an ice dam shield material under the shingles toward the gutter edges of the new roof. This is a strip of material that will prevent water, backed up from an ice dam in the gutters and on the roof shingle edges, from seeping back up the underside of the shingles. This will not prevent the ice dam process, but should prevent it from destroying your interior ceilings, walls, etc.
2. Add insulation on your attic floor and improve ventilation inside the attic. If your attic air space is not conducting heat from the house (through the attic floor) to the underside of the roof underlayment, the ice on the roof will melt more slowly, giving it time to drain properly without seeping under the shingles. This is not foolproof, but is a prudent precaution. Besides, it makes your house more energy efficient. Try using a cellulose insulation and get the federal tax break!
3. Prevent ice dams to begin with. You can install gutter heating strips. When the next huge storm hits, you can plug in the strips so that ice will never form in your gutters again. I have not researched these completely, but it seems that you can also install a sensor that will turn the strips on when conditions require. Go to www.heatersplus.com and search for Wrap-On Roof and Gutter Heating Cable, EasyHeat
ADKS Roof and Gutter Heating
Cable, Danfoss RX Roof & Gutter Deicing Cables, EasyHeat PSR Pre-Terminated Self-Regulating
Freeze Protection Cable for Water Pipes and Roofs, or Chromalox Commercial Grade Roof and Gutter Heat Trace Cable.