Another of my favorite authors is Jane Austen...Pride and Prejudice is the basis for many contemporary books and movies today; a good example is "You've got mail" which even mentions the book.
Some popular favorites for all ages are "The secret Garden" or "A little princess," both by Francis Hodgson Burnett, and who can forget the chronicles of Narnia by C.S. Lewis (these are also in my room, lined up on one of my bookshelves). C.S. Lewis is right up there with J.R.R. Tolkien, and not only because they are referred to by their initials (actually come to think of it, a lot of classic authors go by their initials...hmmm).
The Anne series (and various other books) by L.M. Montgomery are classics, and of course you also have Charles Dickens who wrote a long list of novels such as "Great Expectations," "Oliver Twist," etc, etc.
Some of my roommate's favorites were The Oz series by L.Frank Baum (this is also condensed into one book - unabridged of course - on my shelf because I bought it for Malia last summer) and definitely the classic "Winnie the Pooh" and its sequels by A.A. Milne. We can never forget "Alice's Adventures in Wonderland" or "through the looking glass" by Lewis Carrol.
'The time has come,' the walrus said, 'to talk of many things;
of shoes, and ships, and sealing wax, of cabbages and kings;
and why the sea is boiling hot, and whether pigs have wings.'
I can go on and on creating an even longer list of children's classics including Roald Dahl and Madeline L'engle (a "Wrinkle in Time" etc); however, I have a feeling that more adult and more challenging classics are in demand.
So you could consider "The once and future king" or "Le Morte d'Arthur" which are Arthurian legends. Maybe you would like "The Canterbury Tales" by Chaucer...these are some of the oldest classics in history. Or we can jump ahead to the Victorian/pre-victorian period with the famous Bronte sisters -- "Wuthering Heights" and "Jane Eyre." On the subject of women writers there are also Mary Shelley's "Frankenstein," Willa Cather's "My Antonia," any title by Virginia Woolf, or again Austen and Montgomery.
Some more titles to consider:
"House of Mirth"
"Catcher in the Rhye"
"Uncle Tom's Cabin"
"A little Prince"
"A Handmaids Tale" Margaret Atwood (often considered controversial)
"Treasure Island" Robert Lous Stevens
"Sherlock Holmes" Sir Arthur Conan Doyle
"Swiss Family Robinson"
"Wind in the Willows"
Earnest J. Gaines
Ursala K. Le Guin
Laura Ingles Wilder
Victor Hugo ("Hunchback of Notre Dame" "Les Miserables").
And on a final note you could ask if Natalie Babbit counts as a contemporary classic writer, she wrote "Tuck Everlasting," "The search for Delicious," and other scrumptious books.