Do organs or any structure in the human body shrink/shorten if it's function is no longer useful?
First of all, our appendix isn't 'useless'. Their is a high concentration of lymph nodes (higher than anywhere else in your gut), so it might not be needed for digestion anymore, but it's function somewhat shifted to a more immunological role. 
Secondly, yes there are other organs/body parts that shrink over time. In evolutionary time, look at our tailbone. In monkeys it's still a full tail, in apes it's almost nothing, and in humans it's still present in the skeleton, but not visible on the 'outside' anymore. Probably in a few (hundred/thousand/..) years it will be completely reduced until it is no longer present in the human skeleton (because since we don't have a tail anymore, it doesn't have any function anymore).
Over a much shorter timescale it is also possible. For example the thymus expands in puberty, and afterwards it shrinks until it is almost completely gone.