Considering I've watched about 90-95% of my movies after I was 20, I'm not sure why not. Probably about 80-85% of those are what were "old movies" at the time I watched (and continue to watch). It's a personal choice obviously.
I'm going to try to rewatch all the ones that are a little foggy... and watch the ones I haven't seen... with the exception of Requiem for a Dream... I'll have to think about that one a while...