I think appreciation and enjoyment of older film is a sign of maturity. I went through the stages myself. There was a time in my teens where I wasn't interested in any but contemporary films. As I grew older I rediscovered some of the films I had enjoyed from my youth and the nostalgia was great. Some films, especially cartoons, are superior from the past more so than just about anything available today, or for the past 20 years. Looney Tunes, Droopy, Tom & Jerry, Tex Avery Classics - many of these are 60 years old or more and are IMO the best that have ever been and the best that ever will be. Scooby Doo from the early 70s is far superior to any spin off today.
But I think old films are great, too. Scrooge (1951) is my favorite adaption of Dickens' Christmas Carol. And The Haunting (1963) is one of the very best haunted house films IMO. Even with something like Halloween (1978) or The Texas Chainsaw Massacre (1974), these original films are far better than their re-makes/imaginings/whatever. It is a very rare film where the original is not better, if only for this fact - it is the original!
EDIT - for Amanda and others that think the special effects in old movies look "fake." I can appreciate this sentiment somewhat, but I find it incredibly ironic at the same time. I can't wrap my mind around how something fantastic or mythical can be considered "fake" when there are no real world comparisons to be had! And how do you consider a CGI monster, with actors reacting to it on a green screen, to be realistic? Also funny is that the monsters of yesteryear were many times a guy in a suit, which is much more "real" than one created with computer graphics. Watching a movie with heavy CGI use is to me like watching a cartoon or video game, not a film. Movies like the original Star Wars, Alien, and fantasy films like Krull have special effects that IMO are every bit as good as most in modern film. And if horror is your thing (LOL), then it doesn't get any better than The Thing (1982).