As said in the other recent Tolkien thread, fantasy as an established marketplace genre might not exist. If it did exist, it would certainly be different.
To clarify, people like Andre Norton were certainly writing fantasy before
Lord of the Rings hit the bestseller list, but it was the success of LOTR that made editors and publishers sit up and take notice. Classic fantasy authors like Robert E Howard and E R Eddison were reprinted in paperback, and publishers eagerly signed up writers like Terry Brooks and Rober Jordan to turn out fantasy series that were unabashedly Tolkienesque. And for some years now, I believe, fantasy has considerably outsold SF.
Without LOTR, I'm not sure this breakthrough ever happens. I can't think of any other fantasy that would have shaken up the marketplace the way it did, defining fantasy as a commercial genre. Tolkien is the more important writer in this respect, not CS Lewis. The Narnia books have been steadily popular, but they did not transform the marketplace the way LOTR did. (Anyway, without Tolkien's influence, Lewis probably never writes them.)
Even if fantasy did end up establishing itself in the marketplace alongside SF, it would certainly take a different form, or several different forms. Besides being the book that established the fantasy market, LOTR has also defined that market - it is the "standard" fantasy, so to speak, that has shaped the expectations of the genre. Certainly it defined "high fantasy." It also provides a sort of connection point between, say, sword-and-sorcery on one side, horror on another side, and so on.
Also, as someone pointed out in the other thread, while LOTR may not have been the main influence on Gary Gygax in designing D&D, it was a main influence on players. Roleplaying games might never have taken off. Computer "shooters" would exist - they're basically an offshoot of traditional arcade games - but multiplayer games might not.
Flip side of all this is that LOTR may have short-circuited paths not taken. SF was in something of a crisis in the 1960s and 1970s; writers and fans were looking for new directions to go. LOTR came along and established one. Without it, other possibilities might have been pursued more - alt-hist, for example. While the occasional alt-hist has been around for years (
Bring the Jubilee, for example), the contemporary alt-hist boomlet only really began with Turtledove, I believe. Maybe it would have filled the void left by the non-existence of Tolkienesque fantasies.
-- Rick