-Pride and Prejudice, if you think there's any possibility you might like it.
-A Fire Upon the Deep by Vernor Vinge. Absolutely fantastic space opera from the early 1990's (& won the Hugo in 1993); I think it would appeal to most people who love Star Wars: richly imagined aliens, a compelling plot (w/ some excellent twists), a future that for some reason still has Usenet... Stumbled upon it back in 2008 & it's still my favorite scifi novel. (Ranked below that are Ender's Game and Asimov's Foundation series, for comparison.) Also, if you like Fire, it's got the best-executed prequel I've ever seen: A Deepness in the Sky.
-His Majesty's Dragon by Naomi Novik. Think Patrick O'Brian (Master and Commander), i.e. Napoleonic naval novels, but add dragons. Despite the potentially tacky premise, it turns out that it's executed with lots of charm & grace, making for a really enjoyable light action novel. Probably the best summer trip reading of all the books I'm recommending.
-As I Lay Dying by William Faulkner. Despite people's obsession with Absalom, Absalom! and The Sound and the Fury, I think this is Faulkner's masterpiece. Devastatingly tragic, and makes the best use of modernist literary techniques (a la Virginia Woolf & James Joyce) of any book I've read.
-Dostoyevsky, if you haven't read anything by him. Crime and Punishment is a more manageable length, but Brothers Karamazov is worth the length. To classical music lovers, I usually describe Dostoyevsky as the Mahler (or Shostakovitch) of literature.
-Terry Pratchett's Discworld series, if fairly random, oddball humor mixed with genre satire is your thing. I wouldn't start with the beginning of the series... I'd recommend beginning with Guards! Guards! or Small Gods. I love Reaper Man, too, though for that you probably would need to read Mort first (which I like rather less).