Really good question, and really hard to answer! I'm lucky enough to be known in my family as the person in charge of family heirlooms. Just a month ago I was given my Grandmother's wedding band. I have a mourning brooch/locket that belonged to my great grandmother---inside is a tiny lock of red hair (she lost 2 babies, so I assume it's from one of them). I have a few tin types from that side of the family, too. From the other side, I have a hand loomed wool coverlet from ca. 1870; when my Mom received it several years ago she wanted to cut it into pieces so each of my siblings could have a piece of it, too! Luckily, they all told her to give it to me to take care of. I have a compote from my gr.gr.gr.grandparents' home I have a "gold" bangle bracelet that my grandmother wore to church; it has the teeth marks of her oldest child on it! A great aunt knew I collect dolls and gave me the doll she'd received for Christmas in 1909, still tied in the box, with a note inside to mark the date.
Obviously, I can't pick just one
and there are other things that would take too long to mention.