I was born in 1984, and thus don't remember much of the '80s (having only been five when they ended), but yeah - I still watch stuff from the '80s. My favorite movie ever, Blade Runner, was released in the '80s, and most of the anime and kung fu/Hong Kong action movies that I like were from that period. Of course, I also watch stuff from the '60s, '70s, and even the '30 and '40s (I love me some film noir). So I'm perhaps not the person who will give the most representative of answers to this part of the question.
As to the other part: unfortunately, I do think a lot of younger people now would just scoff at the Millius/Schwarzenegger version of Conan the Barbarian, awesome though it is, for the simple reason that it's "old." For example, I was working at a video store when Rob Zombie's remake of Halloween came out on DVD. I had a number of teenagers express dismay when it was rented out, and when I recommended they rent the original (which is another of my favorite movies) instead, I had at least two respond with, "But that's old."
Similarly, there was an anime group here in town whose meetings I used to attend; I once brought my DVDs of the original Guyver OVAs, and when I mentioned to someone that I'd brought them, his response also was, "But that's old." This guy wasn't even much younger than me - I'm 25, and I know he was in his 20s. No one expressed much interest when I showed up with Beast King GoLion, either.
So yes, the impression I have is that there is already a definite prejudice in younger people's minds when it comes to things that weren't made within the last, say, ten years.