Pre 1900....
To second some of what's already been said...
Huck Finn -- You must, must, must read this book again. This book is 19th century America. This book is American literature. I can't say enough about it. I can't think of any other work which is so emblematic of an epoch and a nation, and at the same time so amazingly brilliant in its pathos, its linguistic virtuosity, and its humor.
Don Quixote -- My only regret in recommending this book is that it's so much better, and so much funnier, in the original Spanish.
Heaney's translation of Beowulf -- Not only does he return the work to a poetic form truer to its roots than earlier translations, but he breathes life into what is, after all, an epic adventure.
Moby Dick -- Perhaps the most brilliant novel ever composed in English. But a virtuoso work, highly referential, not for everyone. Definitely not a must-read for casual readers, but if you love literature and religion, nothing compares.
Gulliver's Travels -- Absolutely hilarious, and as politically relevant today as it was in its time.
Extraordinary Popular Delusions and the Madness of Crowds -- The antiquated diction can be offputting, but there's nothing else quite like it. A true classic, and a fascinating read.
Dickens -- All of what has been mentioned, and more. This man invented the contemporary novel as we know it. A superb marketer who knew his audience and how to craft a book (or a serial) so that it would sell, and also a brilliant stylist and a master of concise description and quick humor.
The Bible -- Also not for everybody. Reading the Bible is a life's work, but well worth the effort, I think. It contains just about every genre you can think of, from liturgy to fable to allegory to ecstatic vision to political allegory to erotic poetry to genealogy to political diatribe to parts lists, on and on... amazingly rich and undeniably of central importance to Western literature. But very hard to understand, requires an enormous amount of reading in secondary texts to make sense of it. Right now I'm re-reading the Torah in order of composition, oldest bits first -- very enlightening... I'm seeing connections I hadn't guessed at before, and debunking spurious connections I'd assumed were meaningful.
To these I would add:
Leaves of Grass -- The foundation of modern American poetry. At least read Song of Myself. Or find a good selection which includes this and the best of the war poems.
Pinocchio -- Don't get anything dumbed-down or abridged. I highly recommend the edition illustrated by Greg Hildebrandt.
The Autobiography of Benjamin Franklin -- It's not the truth... anyone can tell the truth... it's much better than that!
Bacon's Essays -- Even today the man seems amazingly modern. If you're interested in thought and literature, you can't ignore this one. The best of the English Renaissance.