A couple weeks ago, I published a pdf version of Practical Crocheter's Basic S2S Hat pattern, which she first posted here. That original post also included a pattern for a basic top-down hat, and this pdf is that pattern.
A lot of crocheted hats are made in a coil from the top down. This variation of that concept is worked in half double crochet, which is thicker and denser than double crochet, but softer and more flexible than single crochet. You can wear this hat with either the "right" or "wrong" side of the half double crochets facing out. I happen to prefer the look of the "wrong" side, which is what you see in the picture below. Instructions are included for worsted or DK weight yarn, and for infant, child, and adult sizes.