Ooh, yes, I've played this "Humiliation" game before! [And I'm an English literature nerd of epic proportions so my gaps always make me feel guilty...but there's just not enough time to read everything I want to and struggle through things that aren't my cuppa].
Some of my 'shouldas':
Lord of the Flies
anything Faulkner (I can't read his style for some reason - I've tried, many times)
Paradise Lost (I only made it half-way through)
A Tale of Two Cities
Great Expectations
Anna Karenina
1984
Don Quixote
Slaughterhouse Five
Waiting for Godot
Faust
Granted, I'm not sure how much of this list is "high school" reading versus college perhaps, but these are ones I find either commonly referenced or that I want to read, but haven't been in the right frame of mind to do so. I always squirm when admitting to not reading these items, but I have read a LOT of other classics from various periods, not only for my past studies but also personal enjoyment. I still do. I happen to love Austen, Bronte, Hemingway, Poe, Twain, Hugo, Dumas, Plato, Homer, Machiavelli, Joyce (with the exception of Ulysses), Brecht, Malory, Hess, Spencer, Dante, Chaucer, Eco, Shakespeare, V. Wolfe...[it's a long list]
Macbeth. Around here, this seems to be the Shakespeare play that everyone reads in high school, but by switching schools, I managed to miss it.
*holds hand up, hangs head in shame* I, too, have not read Macbeth, though I have read pretty much every other Shakespeare play. And many of his contemporaries. *cough* This is particularly egregious given what my graduate degree is in...I've seen the play performed several times, mind you, but I always seem to skip reading the play.
Some day. Until then, I'd prefer to reread Lear and the Henry cycles.
I've read one Bradbury title, and keep wanting to try more - the style can grow a bit thick, but in a good way.
My personal favorites are Dandelion Wine and Something Wicked This Way Comes. I always reread these two every summer and fall. Personally, I find Bradbury's writing hauntingly beautiful.
Ditto a read of some mythology. I had the Bible and a great deal of mythology under my belt before I hit high school; I think I spent a lot less time looking at footnotes as a result (which likely caused me to enjoy some works others found painful).
I really don't think we all need to read and enjoy all the classics. I don't even think that's possible. [snip] However, I do shrug when I hear people dismiss all the classics as dull and irrelevant.
I think a solid grounding in mythology and the Bible provides much more enjoyment because you "get it" when the author is either referencing these works, or using an archetypal structure and twisting it in a new fashion. Perhaps folks don't always enjoy the classics because there are often nuances to the stories, based in mythology and the Bible, that add a deeper meaning - and if you miss the reference in the first place, it won't hold the same appeal. That's why I still turn to classics I've read before and other classics "new" to me all the time, in addition to more modern works. I like it when it's self evident that an author is well-read and has incorporated that knowledge base, however subtly, in his/her works.
Again, from an SFF perspective, I know some of those references back annoy the heck out of some people. But as a former academic who loved medieval/Renaissance studies, well...I get all geeked out when I understand where someone is getting their story archetypes and ideas, be it Arthurian tropes, history chronicles, or Old English.
I don't begrudge a disinterest in the classics; frankly, though I'm an English lit nerd myself, I hated what I perceived as the classics up until my senior year in high school. My husband, a very smart individual, doesn't enjoy the classics at all. He only recently read Conrad's Heart of Darkness and asked me after finishing, "WHY exactly is this considered a classic?" A very lively discussion ensued, but he's still not convinced. Then again, he can happily re-read Adam Smith's Wealth of Nations, while I try not to gnash my teeth struggling through it.
I think whatever sparks a love of reading and a love of language is the most important thing. If that leads into the classics, wonderful. If that leads into philosophical treatises, economic theory, or heck, every latest crime thriller, mystery, romance, etc. you can get your hands on, wonderful. But I'm rambling and off-point from the original post.