Send a likeness of your kids to your parents so the grandparents can see what their grandchildren look like in 3D. Yes, a photograph would do just as well, but there will be some who prefer the 3D representation.
Grandparents can send their likeness to their grandchildren so that even if the grandkids don't see their grandparents often, they'll still know what they look like.
Cosmetic surgeons can print out a "before" statue, make some changes to the model, and print out an "after" statue to give clients a chance to see what their new faces or bodies will look like in 3D rather than just on a monitor.
Related to the above, "save state" for your physical appearance. If you scan in your face and body and then suffer a disfiguring accident you can use the scanned data as a template for the cosmetic surgeon to put you back together. This would probably be limited, at first, to people like actors and actresses, models, athletes in sports where there's a high risk of facial injury (boxing, hockey, American football), or the military who either have a lot invested in their looks or are more likely to suffer disfigurement due to the nature of their work.
Grave markers that look like the person whose grave they mark, or hollowed-out 3D portraits to hold cremated remains as urns.
On a more whimsical note:
Custom awards. 3D print out an Oscar with an actor's face in place of the blank face. Or a sports team where each player poses for their own custom trophy.
A family with many children could turn them into a set of nesting dolls with each child's doll nesting inside their immediately older sibling's doll.