I picked my faves off wikipedia's 100 classic collection. You probably know a lot of these by their movie versions, which I think makes the books more accessible.
Pride and Prejudice, Jane Austen
Jane Eyre, Charlotte Bronte
The Secret Garden, Frances Hodgson Burnett
Alice in Wonderland/Through the Looking Glass, Lewis Carroll
The Adventures of Pinocchio, Carlo Collodi
Sherlock Holmes, Sir Arthur Conan Doyle
The Count of Monte Cristo, Alexandre Dumas (also wrote The Three Musketeers)
Black Beauty, Anna Sewell (the main character is a horse, just fyi)
A Connecticut Yankee in King Arthur's Court, Mark Twain
The Picture of Dorian Grey, Oscar Wilde
The Time Machine, H.G. Wells (for classic sci-fi, H.G. can't be beat)
Didn't include any Dickens or school reading because I really never enjoyed them.