I've recently started to read more and more classics, but even so my knowledge of them is rather small.
My personal favorites are Pride and Prejudice by Jane Austen, The Scarlet Pimpernell by Baroness Orczy, and the Count of Monte Cristo by Alexandre Dumas. The Three Musketeers by the latter is also one of my favorites.

A Tale of Two Cities is lovely, if I do say so myself.

Les Miserables is all right, but not my personal favorite.

I know most won't call it a classic, although it will become one, but I love Brave New World.

The Picture of Dorian Gray is interesting, but I had to read it several times before I finally understood it to my liking.

My favorite Shakespear play is Much Ado About Nothing, it's just so amusing!