Some people are really showing their youth in this thread!
Perhaps the oldest thing that I've inherited and is more mine than family's is a railroader's pocket watch that, as far as I know, would date from around 1950. Still works; it's mechanically powered and glows in the dark (and is actually the only functioning watch I have, come to think of it). I'm also the primary user of a card table that my family has that dates from the 1930's, but it's not technically mine.
My family has several other aged items, most of which are from my dad's side of the family. Things that come to mind are some 78's that are likely 1940's or older, and a few family bibles from the late 1850's.