I have the small braid of my grandmother's little sister who died of diphtheria. She had cut her hair herself with a little scissor and her mom saved it. We have a photo taken of her just after she cut it and you can see the funny stub of hair behind her ear. She died soon after. I treasure the picture and the braid.
No one has mentioned the wonderful treasure of DNA from a long ago relative. As testing becomes more common, it might come in handy for tracking family lines or something. Some of my kids think it's icky, too, but I think one of them will treasure it some day.