I vote INFP. I love imaginary worlds. I have taken it so far that even though I am not a player myself, I keep reading Dungeons and dragons and Warhammer rulebooks just to get a feel for those worlds.
There are entire fantasy and science fiction worlds and cosmologies inside my head.
I've gone through phases of obsession with fantasy worlds before (primarily ages 8-12) so I'd also vote INTX. Almost all my friends are also INTX and they all have the same tastes that I do in that regard. Warhammer is a good example. Used to be completely obsessed and almost all of the other people I met through that hobby were also INTX.
I am very much a fan of Tolkien, and am consistently thinking of fantasy. I create many worlds and many ideas for D&D and books, but rarely do I put any of it to use or in writing. I also really like science fiction as well.
I do not think that any type in particular would be most into Lord of the Rings. I may like it for different reasons, but just as much as someone with a different type.
I've known an ENTP who was into hobbits and stuff like that. Lord of the Rings was like a sacred book to him to the point where when i presented him a comedy interpretation of it he couldn't have a laugh with me - that was disappointing. And I can recollect another ENTP who was into games like WoW with magic and elves and that kind of stuff.
By MBTI I'd say INFPs are most likely to be into these kind of themes.
I love fantasy and sci fi, I'm always drawn to symbolism like amulets, badges, monoliths, spaceships, planet names and the different aliens, tribes and their belief systems and the things they wear and weapons they use. Not so much into the storylines although they have to be cohesive, its all the creative and imaginative ideas behind it all that I like most. Stargate and Babylon 5 are biggies for me with sci fi but I'll watch almost any medieval/fantasy sorcery and magic type movies.
Personally I like Angela Carter and Kafka on the shore sort of stuff in terms of...fantasy. More a mixture of reality and fantasy, and examination of culture though, than magic and fantasy. And ongoing, or riddle like metaphores. That's seems a slightly stereotypical picture of a more SJish approach (with touches of Ni) to liking fantasy literature.
I'm not a fan of fantasy or sci-fi genre - quite frankly, I often find it very literal and straightforward when it comes writing style. I tend to prefer novels which have a deeper symbolism or make indirect commentary on humanity, the world, etc, but the setting and character need not be fantastical. I do like novels with a surreal aspect, but they don't fall under genre fiction.
When I was a child, one of my favorite books was The Phantom Tollbooth, but that book is clever on many levels. It's more than just a fantasy world.
For instance, I very much dislike Harry Potter & all that vampire stuff. It seems very surface and I find that dull. Of course, this could also be a matter of the level of writing....and it's probably why I greatly prefer literary fiction to any genre fiction.
I don't know if it is common for ENFJs but my brother (also ENFJ) and I both love that kind of stuff. In fact when the last Star Wars movie came out we had to meet up for a movie because both of our spouses don't really like Sci Fi. (Sometimes I feel like SCi Fi and fantasy merge). I like both.