What body parts continue to grow throughout life?
Ear and nose.
The growth of most structures(muscles, bones etc...) of human body stops after adolescence. But here is one special structure called cartilage that continue to grow till death.
Also one important point to mention is that cartilage is present at several sites in our body but mainly the cartilage(softer connective tissues) of ear and nose continue to grow. That's why aged people have larger ear and nose comparatively...