It might not be true that every family has one cool thing about it but at least I can say that my family does.
Sixty-three years ago my father was teaching at Oswego State Teacher's College (now OSU) in upstate New York and developed a friendship with another professor named Roy Lichtenstein. Roy gave us a couple paintings from his trove of over 600 from that period, 1955-1959, and the next year off we went to Muncie, Indiana where my father had gotten a job teaching English at Ball State Teacher's College. (When we were in his studio picking out the paintings I famously pointed to the “Donald Duck” which later sold for a couple million when Roy's pop art career took off.)
Roy went across the river to Manhattan and took one out of a frame where it was hanging in a bank, rolled it up, and gave us that one also. Wherever we went the paintings came with and with each move we rolled up the big one then tacked it on the new wall for the next forty years. (When I hopped a freight train when I was seventeen in 1971 I inexplicably called Isabel, Roy's Ex and mother of his children, went we got to New Jersey.)
We've had the paintings ever since and soon after disappearing with them in 1964 Roy made his name on the pop art scene with a completely different style, recently one of them went for 159 million.
It wasn't until 1998 that I finally convinced my father to get ours appraised and framed.
We grew up with these paintings as the background of our lives in various houses with some stories attached. My father died twenty years ago and my mother recently so the stories are less accessible but may still be around in the family memory.
We recently lent one to an exhibition which was appraised at $35,000 25 years ago and that number has gone up to $260,000 in the interim. But you never know about art: it might sell for way less or way more, a crazy world I know little about.