Ooh! I'll start!

To Kill a Mockingbird
Great Gatsby
East of Eden
Lord of the Rings (if you have any interest at all in fantasy)
Harry Potter series (yes, I'm a HP nerd)
Gone With the Wind
Catcher in the Rye
The Brief and Wondrous Life of Oscar Wao (my students
introduced me to this one)
Pillars of the Earth (love, love, love)
Jane Eyre
Of Mice and Men
The Red Tent
The Kite Runner
Water for Elephants
A Thousand Splendid Suns

Okay, that's more than 10. Not all "classics", but definitely my favorites.