Know them...the inclusion of "Young Frankenstein" throws off your definition of 'classic' for me a bit, since it was made in 1974, a couple decades or so after the period suggested by your other examples.
I'm not a huge early-film buff. I like "Casablanca," but I don't love it. I appreciate "Citizen Kane," but I don't terribly like it. I do like "The Birds," and "Vertigo."
"It's a Mad, Mad, Mad, Mad World" is one of my favorite movies ever, and I love just about anything by Abbot & Costello.
I love musicals and disaster films in general, so if someone's singing or a lot of people are dying, I'm generally happy--so from "My Fair Lady" and "West Side Story" to "The (original!!!) Poseidon Adventure " to "The Blob."
Jumping into the 70's with Mel Brooks opens up a whole new generation of movies, actors, and directors for me. Love most Mel Brooks. The "Airport" movies. Most anything with Jack Nicholson, Al Pacino, Robert DeNiro, Gene Wilder, etc. Moving into 'modern classics' there, though, and I could write for hours. Hell, "Star Wars" came out just 3 years after "Young Frankenstein." And, yes--I was only 5, but I did actually see "Star Wars" in its first run.
I'm generally not a fan of remakes in general ("Evil Dead 2" being one of the few exceptions, and it really is a remake and not a sequel--they just remade it pretty quickly with more money, since the first one blew.) Considering I'm not yet 40, I'm highly offended by remakes of movies originally made in my lifetime. I love Johnny Depp, but Willy Wonka hasn't aged that badly, and Gene Wilder is hard to outcreep, even by Mr. Depp. "Footloose"--unnecessa ry, and just WHY? I love the original, but face it, the world doesn't need more than one version. I'm not even going to more than briefly mention remaking anything regarding Herbie the Love Bug, because then I'll be forced to think about it.