The Time Machine by H.G. Wells
This is by far my favourite classic (so far at least!). I love H.G. Wells. His books are amazing in both imagination and writing style. In addition to being an exciting novel about time travel, The Time Machine also has an interesting theme about social structures. It's also interesting to see Wells take on the future of mankind. While it's not exactly post-apocalyptic, the decline of humanity is definitely there. I personally find it a refreshing change from the modern apocalyptic trends with nuclear fallout and such. Here, we don't know why humanity fell and only see the last remnants of the event that triggered the decline. I also suggest checking out The Invisible Man (which is rather hilarious) and The War of the Worlds.
Dracula by Bram Stoker
Yep, you knew it was going to be on here. I won't spend too much time on this one, but I will say that Stoker is great at maintaining interest and suspense. Even though everyone knows the story, the little clues that mount up to the reveal of the vampire really tease at the reader. It is a great mystery. Also, Stoker's descriptions are amazing.
Frankenstein by Mary Shelley
This one is also a no-brainer classic. I actually read this for the first time this summer (waaaaay too long of a put off on my part) and it was great. I liked how Shelley makes Dr. Frankenstein very intriguing, especially his obsession and later regret of creating such a monster. Also, the character of the monster is fully fleshed out, not a cardboard cutout that is often seen in film adaptations of the book. I personally found the monster a little whinny, but that's just me.
Alice's Adventures in Wonderland; Through the Looking Glass by Lewis Carroll
These two are crazy and creative. Definitely don't read one and not the other! I love how wacky and random everything is in these books and how Alice somehow makes them out to be incredibly normal. She is an unusual girl herself. These books are fun, incredibly silly, and also include catchy poetry. What's not to love?
A Tale of Two Cities by Charles Dickens
I love this book. A lot. It's funny because the first time I read this book (in high school) I hated it while I was reading it. Then, the moment I finished it, I loved it. The way all the parts that seem independent all mix together throughout the story is amazing. Also, all the characters are fascinating and unusual in some way. The very character arc that Sidney undergoes is wonderful and really made the book for me. Rereading it is a lot of fun when you know where all the characters eventually end up.
The Odyssey by Homer
This one is really old! Also, not actually written by Homer, just written down first by him (actually, he was telling it aloud and someone else was writing it down, but anyway). This story is amazing and much better than the Iliad, which I find incredibly boring at parts. It is an adventuring and exploring tale, also including some troubles Odysseus faces once he gets home. I am a huge fan of Greek mythology and I really love how Athene just decides to help Odysseus out because he is clever like herself. Wonderful story. Also, if you want to watch a very loose adaptation of the Odyssey, watch O Brother Where Art Thou? It's a very very loose adaptation but entertaining (plus George Clooney, so what's really to complain about?).
That's enough of a list for now, but I will post more books later on (currently in the middle of Twenty Thousand Leagues Under the Sea). And not just classics. I don't just read stuff that was written one hundred years ago ;)