Just reading what @ultamentkiller
say above, I hesitate to even try to answer this... For someone who does analysis as a career, I'm not that good at some kinds of things. Or at least, I haven't thought that deeply about them. (Which is pretty lame, in this case, for someone who wants to become a better writer.)
But here are a few things I love. Since the OP is about my "favorite story", I have to go to JRRT for much of it.
> Suspense. I love a book where I have to cover the right-hand facing page with my hand because my eyes will
stray over there. The anticipation is just that great. I have to say, I get this more frm spy novels and the like than from Fantasy. But there was some of this in early books of ASOIAF, I think. And from LOTR, you get the scene where the hobbits are hiding from the Nazgul.
> Wonder. LOTR has this more than almost any book I can think of. JRRT imbues everything with this, from the smallest twig to the greatest monument, and from the tinest moment to to the grandest battle. But for non-LOTR fans, read The City of Blades.
> Real heroes. By which I mean heroes who are really heroes and real in their heroism. They struggle, they fail, they screw up, they succeed at terrible cost. Logan Ninefingers, Paksennarion, Taran Wanderer, Miles Vorkosigan, Jon Snow (of the book), Frodo, Sam.
> Surprises/Twists. The litany of dead POV characters in ASOIAF, Gandalf at the Bridge. In some cases, this comes like lightning. In other cases, as slow development: A Crown for Cold Silver just keeps making you say "What?!" (It's not a favorite story, but it has great moments.)
> Delight. The entirety of The Copper Promise
, Merry and Pippin, Tom Bombadil (yes, I'm a fan), Hogwarts
> Rich side stories. In Lloyd Alexander's Prydain series, half the books are a sort of side story to the main epic thread. LOTR is a tapestry of side stories and lovely details.
> Language. I'm with TGC on this one. Lovely, lovely language - by which I don't just mean beautiful. LOTR has it, and Abercrombie has it. Lawrence has it, and Susanna Clark has it.
I'm sure there's more. Every book is different with different delights. It certainly comes down to characters, but I could read The Woman on the Train for characters. In Fantasy, it's the wonder, dread, fascination, and sheer stakes into which we drop these characters that set our stories alight.