Is having Huge icicles hanging from your roof normal?

Icicles = Ice Damming. 

Some are normal but very large areas of ice in the gutters and icicles is not normal. 

It's true that this can be exasperated by insulation issues. Like in a post a week or so ago, sometimes insulation get blown back from the perimeter of the attic. 

As well, this can be cause by a poorly designed roof where two roof slopes direct water to a small area with a gutter.