Based on the comments, here is the list of ways to encourage reading classics. I was going to just put together a list, but I couldn't help commenting along the way. I believe that no "one" of these is the magic way; I think it's a combination of these.
* Anthologies. The one I read as a kid is the Arbuthnot Anthology of Children's Literature, now out of print. A much more recent book: The Norton Anthology of Children's Literature, published last year. I am itching to take a peak at this year's Oxford Encyclopedia of Children's Literature, but it's out of my price range. When considering purchase one of these, remember the purpose as a potential reader is to have a taste of everything, and to be inspired to track down more of a particular author. Another issue: copyright. As you wonder why x isn't included, it could be because it wasn't available or was too expensive.
* Books in good condition. Notice I didn't say new; I am sometimes more enthralled by an old book than a brand new one, but some readers get very turned off by dusty, musty books. If part of what you want to do is entice a kid into reading a classic, why not have the classic look as appealing as the just published book? And the problem with old books is condition; first time I read Pride and Prejudice, got to the last page and it was missing.
* Books with good covers. Check out the New York Review of Books Children's Collections, which has reprinted many out of print (or out of sight) classics, including children's books. We all judge books by the cover, so why not hunt for the classic with the best cover?
*Unabridged and abridged versions. While I tend to side with Roger on this one, I think it's a valid point that a well done abridgment can be a gateway book to a reader. I also think it's wise to not confuse story with words; a person may not be a "reader" but may love a good story. If an abridgment brings that story to the person, where's the harm? My main concerns: it's a well done abridgment, and it's up front and obvious. Nothing worse than a person thinking they read a book when, in fact, they haven't.
*Having the book on the shelf. For libraries with enough space, this may mean shelving the book in different areas (J, if appropriate, YA, Adult, and Non Fiction (the 800s)). And it means parents having books on their shelves. Yes, libraries are great; but it's also great to have a home library.
*Various formats of the story told in the classic; with other formats including movies, TV shows, cartoons, comics, and graphic novels. Maybe it will inspire the person to pick up the actual book; maybe, it will help the reader with an otherwise difficult story. (I swear, the reason I ended up loving Moby Dick was because of the movie versions and comic version I had read before I read the actual book.) Not to mention that classics like plays were meant to be watched, not read.
*Self-expression; wanting to be the type of kid who reads classics. Frankly, I'm not sure what an adult can do to "make" a kid be this type of kid. Tied into this is a certain type of peer pressure; if everyone is reading, and enjoying, a book, you want to, also.
*Reading aloud and audiobooks. Some classics were meant to be heard; and it's another great way to introduce and share in the love of literature. (What's also great about audiobooks -- knowing the right way to pronounce a word.)
*Don't force it. (Encourage, yes. Force, no.)
*Good booktalking. If the book sounds interesting, a kid will want to read it. Which brings us back to the appearance of a book: it needs an appealing cover, to look enticing, and to also have a good blurb.
*A belief that reading the classics is important. While there are certain things adults can do such as chat up their own love of Dickens or Austin, or be the English teacher with the Will Shakespeare statue, part of this is the kid's personality; because just as one kid will be swept up in the love of classics, another may be turned off.
*Buying books, and encouraging kids to buy books. A box of books at a yard sale can be a treasure chest for a reader.
*Good teachers who make literature exciting.
*Letting the reader decide what he or she is ready for. Some "classics" were meant for high school or college age; others are for younger readers. Don't miss out on the fun of age appropriate classics such as Swallows and Amazons.
Thank you all for your comments and insights.