I am really enjoying all the comments from everyone on this topic!!
The quilters in my family are rather "sporadic". On my mother's side of the family, they all lived in/near the "big city", and while their homes were spotless, and their cooking was outstanding, none of them did any type of sewing or quilting. On my father's side of the family, my grandmother was a fantastic sewist and cook, and her sister was also a terrific sewist, and also did many other crafts - crocheting, knitting, basket-making and so on. But, no quilting. However, their mother (my great-grandmother) was ALWAYS in one stage or another of quilting. I can remember having several of her quilts in my home as I was growing up. My sister STILL has the "pieces and fragments" of a baby quilt that Mammy gave her (and my sis is 45 now). My grandfather's grandmother (my great-great-grandmother) was also a quilter, and I have a quilt that she made as one of my most-prized possessions. I had a professional appraiser look at it (he actually had to call Barbara Brackman to help identify the pattern!). I can remember sitting at my grandmother's feet next to her treadle Singer, hand-piecing the scraps she had from making my clothes - I think I was about 5 or 6 - so the quilt bug bit me at a very young age!!
As far as "passing it down", when my kids were little, they both "helped" make the quilts, by picking out colors and patterns, and when I had the hand-quilting frame out, they (and many of their little friends) helped put stitches in it. Will either of them continue with this craft? Perhaps. I gave my daughter my old sewing machine, and she does some sewing on it (pillows, other small crafts), so maybe when her new baby is a little older, she will revisit quilting. I do know that both of them have a high appreciation for the art of quilting.