White powder observed after boiling water in electric kettle for many weeks
It's likely that your home is supplied with "hard" water (that is, water with a high mineral content). These dissolved minerals typically include calcium or magnesium ions (from dissolved calcium bicarbonate and magnesium bicarbonate, respectively). Heating or boiling your "hard" water in a kettle will soften it by precipitating the calcium carbonate as its solubility decreases with increasing temperature. 



This (calcium carbonate) could be the white powder you have observed after evaporation. Hard water should not pose any health risks, and in fact can add some extra calcium and magnesium to your diet. If it's still concerning to you, there are hundreds of products available that can soften your water before you use it, just google "water softener" and you'll be overwhelmed.

http://en.wikipedia.org/wiki/Hard_water