I used to read Tolkien several times within the year, though I haven't read it this year (which is quickly going bye-bye) because of time issues.
However, when I was reading Tolkien yearly/semi yearly it was because he gave me something that other fantasies that I had read lacked. It was...depth...myth...he waded into the MacDonald's sea of shadows, saw one, and described whatever it was that reflected it more clearly than any writer that I had known. It was as if I had tasted ambrosia (for it was true myth though I didn't recognize it) and I wanted more.
I don't believe that I feel LotR as deeply as
Child because I haven't lived long enough yet.
I suppose I come back to it for the various reasons that others have mentioned. I read it because the writing style is good -- the story in and of itself is a very good teacher for writers. For me, it teaches how to write, and how not to write.
Other re-reads:
The Prydain Chronicles by Lloyd Alexander.
A Horse and his Boy b
Peter Pan by J. M. Berry -- it keeps me young at heart. Corny I know, but it makes me realize that life is short...and that we mustn't become like John (or was it Michael?) who grew too old for stories.
The Harry Potter books 
Till We Have Faces by C.S Lewis.
There are more....but those are the main ones. The link that all of them have with Tolkien and LotR is nobility and self-sacrifice. True mythic elements.