Lenora Rose said:
I think it is in part because Tolkien was the start of the fantasy genre as it is today, but for a slightly different reason.
There are TONS of compelling characters out there in the genre now, some as compelling as Tolkien's. But the genre is so big no afficionado will have read every book.
Someone made this comment at a convention regarding Science Fiction, but it's true all around Spec Fic. In the early days, everyone could talk about all the books, good or bad, because there were few enough authors an avid reader could actually keep up with all the books released in a given year. There were this eyar's books, and ahandful of rereleased classics (Dunsany et al), and little else. So everyone knew Frodo. NOW, not only are there all the books released this year, but all the books released last year, and the year before... and every year for the past five decades, and all the older classics. There's no author everyone is guaranteed to have even tried to read. I've never read Terry Brooks. I've read very little Robert Jordan. On the other hand, I would consider Ellen Kushner a must-read, and there are a ton of people who wouldn't touch her books.
So discuss all you like, and nobody will come up with a list everyone can agree on, because nobody will have read all the choices.

Not that it can't be fun to debate (I'd vote for Miles Vorkosigan. Yes, SF, but he's darn close to as compelling as anything Tolkien could do. Vlad Taltos is a good vote though. Robin McKinleys' Aerin was one of my childhood heroines. And there's always today's answer to Alice in Wonderland or Lucy from the Narnia books: Coraline.)
I love old books, AKA Alice in Wonderland. I'm just reading Narnia now.
Tolkien was an odd duck as a writer. He mostly projected character through situations, and not through inner dialogue. The reader is left reading into what Eowyn or Frodo was thinking. With that said, he was very insightful, just not conventional.
I think C.S Lewis is an odd writer as well, but in a different way. I love the idea of Screwtape Letters, everything, but I didn't particularly like his writing style, and felt it could have been done in a more "everyman" format. If I tried to write screwtape, I'd have approached it completely differently. But I must admit, his metaphorical style influenced many writers, including myself.
I think he was one of the first, who wasn't actually speaking from a black arts perspective, who really tries to get into the devil's head in a sophisticated way. I think the portrayal of "pure evil" is an art. In my WIP, I lean a little more Screwtape than Silmarillion, in that you don't have even a seed of noble intentions. However, the evil beings in my Universe have certain elements that might remind some of the Valar. as opposed to demons, but with a great deal more complexity.
Tom Cruise said that he had to get into the mind of a Vampire to portray Leshtat (Spelling???) in Interview with the Vampire. In otherwords, a Vampire doesn't see himself as evil. In his mind he justifies his view, as most people try to do. So, a purely evil being sees virtue as a flaw and a weakness, or worse. To him, "Good is evil, and evil is good", thus, they make perfect political spin doctors.
The funny thing is, pure evil dwelling with pure evil, is actually comical, until you realize your species is the intended victim. But as a third person observer, an entire species of evil creatures dwelling together, without virtue, can't be loyal, can't be faithful, and can't be loving. In otherwords, they can only be motivated by hate, anger, greed, covetousness, or fear of reprisal. But they still have to have some kind of heirarchy, and get along. So, you have constant bickering, backbitting, and undermining, while still trying to accomplish a goal.
Picture a creature, who is something like a Demon with attention deficit disorder. You know he's always going to be late. He's going to get lost, and forget assignments. You almost pity the creature, because you know he's going to get it when the boss finds out how he's screwed up. And yet, this creature has such contempt for your race, that he'd mutilate you and your loved ones at the drop of a hat if he could.