I suppose everyone will have an own definition of what a classic is. Mark Twain put it quite nicely:
"Something that everybody wants to have read and nobody wants to read."
As for books I read which I would label classics and which I did read (apart from all those Shakespeare plays) here are those I can think of right now:
The Little Prince
The Neverending Story
1984
Illiad
Odyssey
A large number of modern language editions of Greek, Roman, North, French, English, Germanic, etc. mythology
Most of the Leatherstockings books (The last of the Mohicans etc.)
Uncle Tom's Cabin
Treasure Island
Ivanhoe
The Hobbit and the Lord of the Rings
1001 Night
All quiet on the western front
20,000 Leagues Under the Sea
Around the World in Eighty Days
The Blockade Runners
Momo
Ben Hur
Dr. Jekill and Mr. Hyde
Tom Sawyer & Huckleberry Finn
The Three Musketeers
Robin Hood
Fahrenheit 451
There are many more books which would be called classics over here, but I doubt many of you would have heard of them as they didn't make the leap into the English speaking cultural consciousness (especially books by Karl May for example).
True to Mark Twain's statement there are really several classics I always meant to read, but never got around to.