It's not really about silver having more value than, say, aluminum or brass. I just love the way it looks. And I love thinking about how silver is made. Even brand new silverware has quite a bit of handwork involved in its manufacture. And I like handmade things.
Old silver has even more personality and attention to detail.
For me, there's just no comparison between a plastic spoon and a spoon that some human being took a hammer and pounded out by hand a hundred and fifty years ago. I love thinking about who made it. And how the world was then. And how many people have used even simple, everyday items over many generations. Silver has history.