Only because most non-fantasy readers are unaware of its contents. It has some pretty hard-core ideas for many kids to digest. It’s a series I only recommend to serious fantasy buffs. Same for George RR Martin’s books. For that matter, most of the books I read I would only recommend to people who really like to read fantasy. (Current reading is Vincalis the Agitator, the prequel to Holly Lisle’s Secret Text Trilogy).
I dont think I can add anything of significance to this list that hasnt already been mentioned, except maybe some of John Irving’s novels. I liked the World According to Garp and The Cider House Rules.
About Philip Pullmans novels, I liked them so much that I read the three books in a few days, if you do read the Harry Potter books, and like them, Id definately recommend these even if they are kids books.
Also, you might like some of the Terry Pratchett novels, I dont think they fall under the category of books that must be read, or even under the great classics, but they are well written, and good fun to read too.
Also Tuco, thanks for starting the thread, Ive now added a whole heap of books to my reading list. 
I would sign on to many of the suggestions here. Especially To Kill A Mackingbird.
For sheer enjoyment, I would nominate Perfume by Patrick Suskind. It is an absolute must read.
I second the Bible, in a modern translation. There are stretches in the middle of the Old Testament that are quite skippable, but make sure you at least read Genesis and at least one of the gospels, and then go on from there.
I don’t think anyone’s mentioned Alice’s Adventure’s In Wonderland and Through the Looking Glass, but it’s a must-read. I recall hearing that this is the third most often quoted work in the English language (after the King James Bible and the works of Shakespeare). Its incidents and characters get alluded to all the time. It’s easy to read and very funny.
Get yourself an anthology of poetry/literature and browse in it whenever the mood strikes you.
You might want to check out a thread from awhile back: Recommend books for 10th grade boys who don’t like to read. You’re a bit older than a 10th grade boy, but that thread does contain some interesting suggestions about where to “get started” reading.
Everybody should read the MSTings of Stephen Ratliff’s “Marrissa” storys [sic] at least once before they die.
Correction to the above link:
My primary list of fiction books I enjoyed, and can’t imagine not having read, is:
Cryptonomicon
Terry Pratchett
Lord of Light/early Amber Chronicles
Tolkien
Three Men in a Boat
Hornblower
HHGTTG
TKaMB
Animal Farm/1984 (?)
Dune
Watership Down
Three Musketeers
Name of the Rose/Foucault’s Pendulum
Ender’s Game
I freely stipulate it’s slanted to me, but there you go. You asked. Unfortunately I’ve missed a lot of the obvious ones because they’re SO obvious I didn’t even think of them. Like the bible.
A grab-bag of wider suggestions:
Reading some non-fiction stuff is fun. Someone suggested a good cyclopedia. Sometimes I just go to wikipedia and hit ‘random’ until I go ‘Ooh, that’s interesting.’
Also, look stuff up. If someone says “You haven’t read…” don’t be ashamed - ask them why it’s good. Ask where you should start. Go and find a review and see if you’d think you’d like it. The same applies to facts and vocabulary - if you look it up once you’ll remember it, otherwise you never will.
In a similar vein, jot down whenever you think you should read something.
Don’t be afraid to not like something. You don’t have to like, or dislike, Julius Caesar, but it’s good to have had a look and have an opinion. Some books you just won’t get. It’s ok to quit at first, but try to go back later, and find out why other people like them. Sometimes I’ve read a book and just ‘not got it’ and years later suddenly clicked and realised it was really good. Sometimes even quite famous books simply aren’t that good.
Are there any books, films, you like? You could ask people to suggest something similar.
Like Hell they aren’t “must reads!” 
I’m inclined to agree with js_africanus that if you’re not a big reader, the classics may be a bit tough on you. Some of those books take more dedication than the casual reader wishes to expend.
I think you should start with fluff. Go for what you like. You can find books on all sorts of fascinating topics. If you’re a sports fan, read a biography of a famous athlete. If you like hiking, or adventure, read one of those non-fiction lost-in-the-wilderness-struggling-to-survive books, like Into Thin Air. If you like movies, read a biography of a movie star.
History is also a great subject. Read that An Incomplete Education thatJurph suggested. Not only is it a fun read, but it will give you some ideas of subjects you might want to read more about. Books on the history of everyday objects can also be fun, and fascinating.
Ease yourself into the habit of reading. Don’t make it a chore. Try to set aside some time each day for it-- right before you go to bed is a great time. If you find yourself getting tired of it, or bored, try another book. Take your time and enjoy it.
In time, you can get to the classics. Other books will eventually lead you to them.
Don’t be afraid to ask for advice. You can always start a thread if you’re interested in a certain subject, but are unsure which book to choose. We love book threads around here.
I just looked over St. John’s list of great books, and it turns out that I’ve read all of them! Oh, yeah: that’s because I graduated from St. John’s. Silly me.
Let me tell you the second most important thing* I learned at St. John’s: you’ll get a lot more from any book by discussing it with other people. So I won’t recommend any particular book, but suggest finding a good book club or discussion group.
You’ll be surprised at how much more you see in a book when you bounce your impressions of it off of other people. You may even want to go back and read it again. Do it! Better to understand one book well than to have cast your eyes over ten that made no lasting impression.
Finally, I strongly disagree with others who’ve recommended modern translations of the Bible. Speaking as an agnostic/atheist, I say find a good annotated edition of (or based on) the King James version. It’s one of the greatest works of literature of all time, it’s not all that hard to understand, and its beauty makes it worth the effort.
- The most important thing I learned at St. John’s: NEVER draw to an inside straight.
That’s why I think Vonnegut is such a great author to read. Slaughterhouse Five, for example, is pretty deep, yet it is a fairly easy read. That is one of the few books I actually read before I started taking Ritalin. All his books that I’ve read come in short, interesting packets and leave one thinking and wondering. (If the OP reads Slaughterhouse Five, I’d suggest immediately following it with Terry Pratchett’s The Carpet People: Both books feature main characters who interact with an alien race that see time in the same way we see space, but how the authors treat each race’s perception and understanding of free will is different. Paradoxically, one gets to engage in a fairly deep conversation nested within two books that are ostensibly fluffy! Brilliant!)
So I have to second the question to the OP of what he (I’m assuming that he’s a he) has read and has liked. There’s nothing wrong with getting into sci-fi, westerns, mystery, or Harlequin Romance as one starts out. Just enjoying reading is the big thing, IMO, and one will find gems here and there in lots of unexpected places.
My all-time favorite book is Machiavelli’s Discourses on Livy. I have the old, out-of-print edition that comes in two volumes where the translaters end notes detailing the historical references takes up most of one volume and some of the other. One must either read with two books open, switching between the two, or read just the one without having a working knowledge of the history to which the author refers. On top of that, one must deal with the goofy anachronisms of language and translation left over from a 16th century text. The thing is, I could have never enjoyed the book if I hadn’t spent so much time reading fluff and building my reading muscles for a few years before hand.
Follow JS Africanus advice. I can’t believe some one recomended you “Don Quijote”. I read it in spanish, of course, and it’s a very difficult read.
Avid Dostoievsky, avoid Hemingway, avoid Victor Hugo, Chaucer, in short avoid those books that are considered our “greatest classics”, the greater part are very difficult.-
Then ask yourself what is your favourite genre? (you haven’t read a lot, but I suppose you watch TV and go to the movies), Comedy? Drama? Science fiction? Epic?, etc.
After you have decided ask around. You want comedy? Try Douglas Adams or Terry Pratchet.
Science fiction? “On the Beach” (an apocaliptic masterpiece, and one of the best books I have ever read). John Varley is a very gifted author, for a very good time travel experience try “Millenium”.-
Drama? Both Wilde and Shaw wrote masterpieces. “The importance of being earnest”, “Arms and the man”, or everyone favourite “Pygmalion”.
Fantasy? George R.R. Martin’s “A song of ice and fire” series are excellent, you couldn’t start in a better place. Zelazny’s “Amber chronicles” is another great choice. If you want to start with the master himself, Tolkien, read “The Hobbit”, LOTR prequel and a masterpiece in it’s own right.
A true well read person can’t do without poetry, search the archives and you’ll find thousands of recomendations.
I disagree. The politics, characterizations, and even the sheer lengths of the books are not what I’d recommend to someone just getting into reading, let alone fantasy. I started my love of fantasy with the first three books of the Dragonlance saga. I would never have been able to get into fantasy books without having read that first. My husband almost never reads fiction (except as it relates to a D&D game), but if he expressed an interest in a fantasy novel, I would never hand him Martin. I’d probably start a new fantasy reader with Eddings.
Ah, but fluff is in the eye of the beholder. I found both Vonnegut and Robbins to be difficult, find Jane Austen to be delightful fluff.
This is going to address methodology rather than specifics.
I’m going to suggest something odd, and that is doing some of this on audio. Audio made Tolkein a real pleasure rather than a “who is this whats his name and do I really need to read all this damn poetry.” Audio is nice if you have a long commute and need to drive.
I’ll also suggest letting yourself wander, but letting the books tell you where to go next. Don’t start at the top of a list and go down in alphabetical order. To Kill a Mockingbird is great fun - more fun if you follow it up with Truman Capote’s In Cold Blood and know that Capote is the model for Dill and that Ms. Lee did some of the research (and may have done some of the writing) for In Cold Blood. Both are classics. Likewise, Pride and Prejudice is fun, and makes reading Bridget Jones Diary right afterwards even more fun. Sherlock Holmes is, of course, classic - and followed by Agatha Christie and then maybe Dashiell Hammet, you can get a feel for the whole detective/mystery genre.
Don’t be afraid of children’s lit. Especially starting out. If you haven’t read Tom Sawyer or Treasure Island they might be a good point to start - Treasure Island especially before you start on some of the same era classics.
Do a little reading about your reading - you can come here and get opinions. Tess may be a classic, but its depressing, difficult and really a pain in the back end. Not a place I’d start. I almost killed myself setting out to “read the classics” Madame Bovery, Tess, Heart of Darkness - not a combination for a Minnesota January.
Also, think about Cliff Notes - they aren’t just for cheating your way through Literature Class. Or websites that do the same things (there are a lot of them out there). Les Miserables is a fantastic book, but Cliff Notes made it much easier to get through. Good movie adaptions (Scorsese’s version of Wharton’s Age of Innocence, for instance) should also be part of the methodology - if the goal is to gain cultural literacy and not necessarily to read a zillion pages.
If you get the urge that you need to read something by Hemingway, The Old Man and The Sea is popular (because it’s extremely short), but I recommend For Whom The Bell Tolls. It’s one of my favorite books of all time, and is very dissimilar to the rest of his stuff (which many hate).
I don’t have too many suggestions, other than to test out as many different authors that you can - then you can focus on a particular area that you enjoy.
Sometimes, I will see a movie, and then be inspired to read the book it was based on… but you have to go the book with the understanding that it is an entirely different thing from the movie, and not be disappointed or confused by the changes.
Actually this is a pretty good advice. If you like the movie, in most cases, you’ll love the book. Even better, also in most cases, the book is much better that the movie (even if it’s a great one). Another advantage of following this advise is that the reading will be easier.
For example: After watching Liam Neeson, Geoffrey Rush and Uma Thurman’s “The Miserables” I finally read the book. It’s a huge book (almost 1500 pages) full subplots, etc. But I didn’t mind because, having watched the movie, the basic plot and the basci characters were already “clear” for me.
You were expecting anything else?