I've always felt that "classic" wasn't restricted to a specific time or period in history, whether you're talking about movies or art of really anything else. To me, "classic" means that it has withstood the test of time. It's still relevant and involving. Everyone knows Shakespeare, but how many have read the works of Bacon? One has stood up to the test of time, the other not so much.
Films later than the around 1960 or so are frequently dismissed from the "classic" list for a lot of reasons. Some feel that there has not been enough time to truly seperate the great from the also-rans. Some may take the "they don't make 'em like that anymore" approach and simply discount anything outside their preferred era. Some may have more arcane reasons, but what it essentially comes down to is the fact that "classic" is essentially an undefined term; it means many different things to different people, and none of the definitions are necessarily wrong.
To me, a "classic" film is one that has some ephemeral quality that sets it apart from the rest of the herd. It's a film that you know will still be with you in a month, that keeps creeping up on you over the coming days and weeks and keeps sparking some little thought or idea. It's a film that stays with you. I see a lot of movies; I love 'em, especially adventure films or wacky comedies or horror. My wife will claim I hate certain kinds (romance has never really appealed to me), but to be honest, if a film resonates with me, if after I see it I feel a sense of ownership of it, if I feel like, in some way, the film was made just for me, it really doesn't matter what genre it is or when it was made, it's a classic.