Some time ago I read some postings about the different categories within the fantasy field, and now I can't find that discussion,  The only term I can remember is "Urban Fantasy", and I can't recall what that designated.   As my DW has pointed out several tinmes, I have a mind like a steel sieve.  Would anyone be willing to give me an idea of the different categories, and roughly what fits therein each?

Well, to answer your specific question, to me urban fantasy is characterized by fantasy elements (usually magic and/or magical creatures) in a modern, urban setting. A great example of this is Charles de Lint's Newford stories and novels. It overlaps heavily with paranormal, though paranormal usually sticks more to the magical creatures than magic itself (not always, just often -- lots of vampires and werewolves) and tends to focus a little more heavily on sex and romance (I believe the term "paranormal" originated in the romance field, but publishers have been blending it because the "paranormal romances" were really just urban fantasy that did focus on romance more than an author like de Lint does).

As for other fantasy subgenres. . . Wikipedia unfortunately doesn't have a nicely organized page defining them the way it does for science fiction, but the ones it lists are:

Alternate history/historical fantasy, which would be fantasy that is set in a recognizable historical milieu that is different from historical fact in that it includes fantasy elements. For example, Susanna Clarke's Jonathan Strange and Mr. Norrell.

Dark fantasy, which is a combination of fantasy and horror.

Fairytale fantasy, which is retelling of myths and folktales. For example, Robin McKinley's Beauty and the Beast retellings, or the series that Ellen Datlow put together.

Fantasy of manners, which is either identical to or heavily overlaps mannerpunk; it's often described as what Jane Austen would have written if she wrote fantasy novels. Ellen Kushner's Riverside novels are a good example of this, and the subgenre often has little magic in it.

High or Epic fantasy, which is what Tolkien and all his imitators wrote; it is set in an invented or parallel world, features epic struggles between good and evil, often features one main hero and a quest structure, and often lends itself to a series.

Sword and sorcery, which is the other sort of mainstream fantasy; it too features heroes and high drama, but its focus is usually personal rather than epic -- rescue missions and revenge tales are more common than the save-the-world theme in high fantasy. Michael Moorcock's Elric saga is sword and sorcery.

Heroic fantasy, which is a mix of High fantasy and Sword and Sorcery.

Romantic fantasy, which is fantasy that uses many elements and conventions borrowed from the romance genre. Most of Sharon Shinn's writing fits in this mold.

Urban fantasy, which I described above.

Science fantasy, which is fantasy stories that have a veneer of science fiction about them; they often have supernatural elements that they purport to explain using science, but the science is wholly made up for the story. A subgenre of this is the Dying Earth subgenre, which is characterized by a setting at the end of time when natural laws are breaking down. M. John Harrison's Viriconium and Gene Wolfe's Book of the New Sun are in this subgenre. However, it does not include (at least under most peoples' definitions) novels like Marion Zimmer Bradley's Darkover novels or Anne McCaffrey's Pern novels because, despite the presence of archaic elements in both, telepathy in the MZB and dragons in the McCaffrey, these elements have scientific explanations (both are set on lost, low-tech Terran settled worlds; the matrices are technology in the Darkover novels and the dragons are the product of genetic engineering in the Pern novels).