When I hear "classics" I think of anything older that is described as "classic", though I took a class titled "Classic Literature" once and it was all ancient Greek and Roman stuff like The Aeneid and The Odyssey (both were pretty good, but dense reading to say the least.) Not sure what you're looking for, but here are some I like:
My favorite has to be Crime And Punishment by Dostoevsky. Surprisingly, despite its length and reputation, it was a pretty easy read and once it got going, it kept my interest well through to the end. My only critique is that the entire book is over 3 days and then the epilogue rushes through a span of a decade. Though, I think this is because the book was originally a series of short pieces published periodically in some newspaper. I guess when they went bust or got bought out or whatever, Dostoevsky had to wrap it up quickly.
Other recommendations: anything by Mark Twain, Edgar Allen Poe, or Shakespeare. The Alice in Wonderland and Wizard of Oz books are good as well.
Almost all classic works can be found for free online, especially if you have a Nook, Kindle, tablet, or smart phone. You can download 'em from the Google Books app or whatever.