At the risk of being a devil's advocate...

I'm definitely in favor of reading the classics - I was an English major, so I read my fair share and grew to love them. But now, though I'm not a parent or teacher, I do work with kids in the classroom and so many of them say to me that they would not read if they didn't like the book. 

Classics are great - they're classic for a reason. But not everyone likes them. Some kids prefer other kinds of stories or other kinds of writing. So when they're required to read books they don't like in school, they begin to develop a dislike for reading in general. Then, when the time comes that they can read whatever they want, they choose not to b/c at that point they've learned to not like reading. 

I don't suggest getting rid of the classics altogether. But there can be a way to work them in. For instance, if kids liked the Percy Jackson series, maybe getting them to read nonfiction about Greek mythology and history could eventually lead to The Odyssey and the Iliad. Or if they like monster and vampire stories, find a way to introduce Frankenstein and Dracula. 

If the choice is between reading whatever they want and not reading at all, certainly we'd prefer having kids read something - even if it's not what we would choose for them.