This was a question in Quora which made me think about the watches I collect.
I cannot really explain but there is a certain charm about old watches - even the cheaper ones. It depends on your taste but I like the hand winding steel watches with doomed plastic crystals. I also like the unique and eccentric watches like the Tissot stone watches and brands that do not exist anymore like Favre Leuba and old Indian HMT watches. I like reading about their history and sometimes wonder about the guy who once used the watch to tell time.
When I was a kid, my father used to wear a cheap solar powered Bular watch and I really liked it. It is now in my collection with the crystal all cracked but I really like it because of the sentimental value.
I have also noticed that there is a nostalgia among people for everything vintage or classic and have noticed the classic Casio gold digital watches on the wrists of a number of stylish millennials. Of course, the watchmakers have realised this phenomenon and many including Seiko, Omega, Tudor, Tag Heur among others have all recently reintroduced many of their old designs, of course with a modern take.
Coming back to the question, different people like vintage watches for different reasons. Many collect them as investments, some collect them for aesthetic reasons, others for sentimental reasons, etc.