Most makers do not require filtered, soft, or distilled water. Even so, we recommend that you use some type of filtered water. Our preference is reverse osmosis (RO) water, as the RO process removes the highest number of contaminants from your drinking water, as we discuss in our article The Best Water Filters to Buy (And Why You Need One).
Not only is filtered water a much healthier choice--all of your drinking water should be filtered--it will also help your ice maker go longer between cleanings, and last longer in general because there are fewer contaminants to muck up its machinery.
Your ice will also taste better, particularly if you have an RO system that adds minerals back into the water; you can also do this manually with a few drops of remineralization additive or just a tiny pinch of sea salt.
For some makers, like the KBice model we review below, filtered--or at least soft--water is mandatory.