Ice damming is from warm air in the house leaking up under the roof around the eaves causing snow to melt and then ice dam cause it can't go anywhere. First thing is to address the air leakage and seal around the attic perimeter and check to make sure you have enough insulation there also (r-30 to r-38 depending upon where you are at). Make sure any insulation does not cover or block air flow to any soffit vents. Problem areas seem to be near dormers.
If you are in a snowy area and you have places on your roof(or the entire roof) where the snow melts but it doesn't on your neighbors means you have heat leaking through the ceiling and the roof melting the snow which means you have inadequate insulation. The snow should melt from the sun and not from heat in the house if your attic is properly insulated and vented.
If you are where it is going to have sub-freezing temperatures for some time and are worried about ice dammed water leaking in the house, then hook up a water hose to your hot water heater with a helper to control the drain cock valve. Hot water will melt ice fairly quick. First sweep off any loose snow though. Since hot water can refreeze fairly quick it must have a place to go. Start with running a stream of hot water on (up&down) the downspouts. When a pathway opens in the downspout, then run some down inside it. When open then clear the gutter and when clear then the roof. Depending upon the size of the house and ice damming area, this may take a while since the water heater has to reheat every so often.
I know some places that put heat tape in their gutters and down the downspouts to keep them open in the winter. You might want to check to make the gutters slope properly towards the downspouts.