Within the last couple of years, I have re-read Great Expectations and A Tale of Two Cities and loved them both. I had read them in high school and liked them, but I really enjoyed them as an adult. You get totally different things out of a book as an adult. Life experience gives you a different perspective.
Regarding high school kids, it seems to vary all over the board. My 16 year old, 11th grade daughter, reads and enjoys very challenging classic books. My son, who is a year and a half younger doesn't enjoy reading much at all and never has. We have to make him read the required reading books for English classes.