Depends on what you mean by classic and which continent..
so i am cheating, too!
OK, Great Gatsby gets a vote for American classic, but also The Bluest Eye by Toni Morrison, for modern American classics...
For British, I think Great Expectations is one I couldn't have lived without reading.... just a great story of being who you are, not forgetting who made you who you are, and that sometimes things don't turn out the way you want them to, no matter how hard you try... i read this kind of late in life, but it helped me deal with disillusionment and disappointment in a time when i really needed that help...