[Pitchwife]

Great topic, onewhitetree! And I absolutely concur about Byatt's Possession - a great and memorable read, and I like to think Ash's poetic use of Northern mythology would have delighted our Professor.
Among contemporary fantastists, my top three are Ursula LeGuin (who has been mentioned above), Stephen Donaldson (for narrative technique, character portrayal and piling up any kind of setback imaginable against his protagonists until the final breakthrough) and Patricia McKillip (who has a poet's skill with words - somehow the fantastic in her books seems to just naturally emerge from her use of images and metaphors).
As for contemporary non-fantastists, the most satisfying read I've come across for some years was Stieg Larsson's Millennium Trilogy - the end of Vol. 3, where a damaged and handicapped but strangely loveable character (I have a weak spot for those), with a little help from her friends, 'beats the system' and is vindicated against seemingly impossible odds, comes very close to Tolkienian eucatastrophe for me.

But if you go for sheer daring, scope and ambition, I'll have to mention two contemporaries of Tolkien's rather than of ourselves - both neglected modern classics, both unmistakeably original, and both also sharing our Prof's tendency to write books the size of a brick.
First, John Cowper Powys, author of (among others) Glastonbury Romance, Owen Glendower and, most notably, Porius: A Romance of the Dark Ages, an historical novel set in the days of Arthur and Merlin (both of whom are prominent characters in the book). Here we have an author who was just as fascinated with the mythology and history of Britain from Arthurian days to the late Middle Ages as Tolkien, but approached it from an entirely different angle - either (in Glastonbury Romance) using it as backdrop and subtext for a contemporary plot, or (in the other two) examining the characters of history and myth with a depth of psychological introspection comparable to, say, Dostoyevsky, while maintaining a firm connection with the supernatural. In Porius, especially, the thoughts and feelings of his characters, the natural changes in the landscape surrounding them and the stuff of myth and legend just seem to blend seemlessly with one another. Try to imagine D.H. Lawrence (the psychologist of the unconscious, not the sex-prophet) rewriting The Mists of Avalon, and you'll get a faint idea of what Porius is about.
Then, in my native German tongue, there's Hans Henny Jahnn, author of Fluss ohne Ufer (Shoreless River), a fragmentary novel trilogy which draws you into a world (or, what's the same to me, presents a compelling view of our world) as idiosyncratically the author's own as Tolkien's Middle-earth - although as far removed from Tolkien's faith and eucatastrophe as you can possibly get (Jahnn's credo can more or less be summed up by a famous quote from the novel "It is as it is, and it's terrible"). Here, Man (and it's primarily a book about men, which may deter some female readers - Jahnn was your classical closeted homosexual) is just a creature among creatures, floating on the subconscious current of hormonal processes that defy any rationalization. At the same time, the whole book is imbued with a deep, fierce love of nature (including an uncanny skill at describing, or rather evoking, nature and landscape) and compassion for all her suffering creatures that I can't help but think Tolkien would have sympathized with, whatever the philosophical differences. Unfortunately, as far as I could find out, only the first part (Das Holzschiff / The Ship) has been translated into English - which reveals about as much of the whole as The Hobbit does of Middle-earth; but those of you who can read German might give it a try - either you'll be exasperated and throw the book into the corner after Part I, or you'll be hooked for a journey to the dark side of the human mind.