watch movies that aren't current? Here's my data point.
I took a new job in December, and my new team has a 23-year old whippersnapper. He hadn't seen The Matrix, which was for a certain class of nerds The Most Important Movie Of Its Time. It also didn't feel like it came out that long ago, but of course by the time he had graduated college it was ten years old.
To see if this was unusual, I looked up the top grossing films of 1992, as well as the top rated movies on IMDB. There's no direct analogue to The Matrix on either list, but of the action/nerd/scifi-ish movies I had seen Batman Returns, Wayne's World, Dracula, Reservoir Dogs, Sneakers, and Army of Darkness but not Lethal Weapon 3, Unforgiven, Patriot Games, Under Siege, or Alien 3. So, 6 out of 11.
Obviously my anecdote here is by no means authoritative. I assume that with more media sources generally, there's more dispersion of media consumption. But I'd guess that the Kids These Days are still watching "old" movies, just with a wider variety. Surely there's a Masters' thesis lurking in here somewhere.