I don't know. There's a kind of analysis that will lower enjoyment, but I think that's the kind of analysis that tries to detach the 'hidden content' from the 'surface content.' That's just a poor way of looking at literature, in my estimation. I mean, people analyze books every time they read one--we just don't call it 'analyzing'. Taking a closer look at the work, tossing it against other books, comparing styles and themes--I think these are perfectly legitimate things to do to a work of literature. If nothing else, they help you remember the things you read.
Anyway, I was planning on doing an independent (tutored) study this summer on contemporary American poetry. I decided to call it off on account of low funds, but I still ordered all the books from the list my prof and I compiled. So far, I've read Traveling Through the Dark by William Stafford, and I'm in the middle of The Freeing of the Dust by Denise Levertov. These are both really good, and lots more accessible than I think the casual reader assumes of modern poetry. There's a whole bunch of books left on the list, and I probably won't get through them all this summer... Don't have that list with me now; I'll put more up later, maybe.