I quite like the old Showa era Godzilla movies
(well, all the Godzilla movies). They're cheap and tacky but I love 'em...Even the bad ones have enough absurdity to be enjoyable. I THINK they may be the oldest movies on my movie shelf.
The Gamera series was pretty decent too. Largely for the same reasons I find Godzilla appealing.
In fact, I kind of just love any of the old kaiju movies. The effects were terrible, you can tell that it's a man in a rubber suit with some laser beams drawn straight onto the reel with a pen, but there's just something about them that's so appealing to me. Then again, I've always found practical effects massively more appealing than CGI and watching older movies where they were still working out more convincing ways to do things fascinates me, not to mention a guy in a rubber suit destroying a miniature Tokyo looks far more convincing to me than a CG monster knocking down CG buildings.
Unpopular opinion, films that came out after the 60's can't be called old or classics.
That seems a bit arbitrary.
I think we have a good idea of what movies are going to be around near forever much sooner than 70 years, typically the definition of classic, something that's regarded as high quality over a long period of time. 'One Flew Over the Cuckoo's Nest', 'Pulp Fiction', 'Shawshank Redemption', 'Green Mile'. These aren't movies that are going to fade into obscurity or the general consensus suddenly decide they're terrible, we don't need another 20 years to know that.