To offer a contrasting opinion: I saw the first episode and some fragments of others, and was so put off that I felt no desire to see more. And no, I have no problems with incestual or homosexual themes. No, what made the show unwatchable for me is exactly the surrealism and bizarreness that others like - normally I love such things, Brazil is my favourite movie ever. But in the case of Utena it looks to me like style over substance, masking underlying shallowness and/or lack of a point - similar to Evangelion and Lain, only much worse and with no positive points to compensate. I mean, here we have all these kids sprouting incredibly pompous rhetorics about "revolutionizing the world", but all they ever actually do is the same kind of meaningless social games you'll find in any random US highschool. The scenario also completely lacks a believable or interesting background. The whole show is too bizarre to be immediately acceptable, and not bizarre enough to take it as comedy or believe in the existence of a good explanation

I'm sure that fans of the show can tell me that all of this has a good reason and everything gets much more interesting later on, but sorry, it was just too crappy for me to give it the benefit of the doubt or a second chance.