+1 for anything by Mark Twain, especially "Letters from the Earth".
Quality hardbound editions of The Hobbit and Lord of the Rings would deserve a place on the shelf.
"Watership Down" would make my "classics" list. So would "Alice in Wonderland".
Anything by Terry Pratchett, a true master of the English language with the kind of warped humor that should appeal to all CH denizens. Might as well add Douglas Adams to that category. Granted, these authors aren't dead yet so they might not qualify as "classics". But they will be someday.
Classic science fiction ranks high on my list:
Brave New World
The Foundation Trilogy
War of the Worlds
A Canticle for Leibowitz
Fahrenheit 451
Ringworld
Snowcrash
Journey to the Center of the Earth
I, Robot
Childhood's End
Ender's Game / Speaker for the Dead
The Time Machine
Stranger in a Strange Land
1984
The Martian Chronicles
The Lathe of Heaven
Dune
Neuromancer
Do Androids Dream of Electric Sheep?
Slaughterhouse 5
Flowers for Algernon
Admittedly, some of these barely qualify as "classics". More accurately, they could be described as being written in the classic
tradition: big ideas brought down to human level.
BTW, "Idiocracy" was stolen from a Nebula-winning short story by CM Kornbluth called "Marching Morons".