There are so many varieties of crochet hooks that it was difficult to determine the best way to categorize them. Perhaps the most sought after hooks are the figurals (see my iantiqueonline figual crochet hook article), followed by floral/plant depictions and other fancy-carved ones. My personal favorites are the ones I call "gizmos", or the ones which were designed (and often patented) to solve a problem. These include double hooks, screw-on hooks, tambour hooks (Although tambour hooks are actually a type of embroidery tool, but when crochet became popular they were re-purposed for doing crochet.), folding/pivoting/swiveling hooks, sliding/retracting/extending hooks , hat-pin-like hooks, and Susan Bates hooks with Clipson Stitch-Retaining Clips. There are others I refer to as "plain" hooks of all materials, which include most, if not all, Afghan hooks, as well as non-inflammable crochet hooks.
I plan to add the website addresses for many talented crochet hook artists here within the next few weeks. If I already own a hook by the artist, I will seek his/her permission to post a picture here with the website address.