I saw this question pop up at the top of my referrer logs yesterday, so I guess it's popular, so I thought it would be fun to make a post out of it and try to answer the question.
My first thought is to answer, "It's self-fulfilling. Every exposure to Shakespeare you've ever had has been telling you how difficult and boring and irrelevant he is, so naturally from the moment you cracked open the book, you thought "Wow, this is difficult and boring and irrelevant."
Let me put it in perspective. My daughters, 3 and 5, understand Shakespeare.
Do they understand the words, or the themes? No, of course not, that'd be silly. But if I asked one of them to recount for me the story of "the girl on the island" they'd be able to tell me that Miranda lived on the island with her daddy, who could do magic, and there was a fairy named Ariel and a monster named Caliban....and so on.
My point? People start in on Shakespeare from the wrong end. They start with Act I, Scene I, line 1, word 1, and say "Hmf, I can't understand it, I'm screwed." They lose the forest for the trees.
I say work it backwards. Learn the story, by whatever means necessary. Learn the characters, understand their feelings and motivations. And then you'll find that the words are a bit easier to understand.
How do you do that? Well, subscribe to this blog, for one :). And I'm only half joking. I could point you at "No Fear Shakespeare" and any other number of books that attempt to translate Shakespeare's words into more readable modern English, but that's not my point. My point is that to understand the stories you have to break it down well beyond the words and get to the characters themselves. Romeo's a horny teenager whose girlfriend won't give it up. Hamlet's dad died, and he can't stand his stepdad. King Lear wants to grow old and die in the comfort of knowing his children love him and will take care of him. There are *people* in there, people. If you're so busy concentrating on the rhyme scheme and pronunciation of the words, you're making it too hard for yourself.
I could write all day on this subject, but I don't have time here at work :). Maybe we can get some discussion going in the comments? Show of hands, how many people out there think that Shakespeare is hard? How many think it's easy? Why?