DNA fingerprinting is used in quite a few areas in the medical field!
Identification of twins
One of it's main uses is to tell if twins are identical or fraternal at birth. Sometimes parents don't know for sure if infant twins are identical or fraternal. Babies look similar when they're first born, especially twins, even if they're aren't identical. So parents can choose to take a DNA test to see if the children's DNA is the same, clarifying if twins are identical or fraternal.
Paternity testing has become highly demanded in today's society. Mothers get accused of cheating and their partner's demand a paternity test to make sure their supposed "child" is actually theirs. As well some women may have just come out of a relationship and can't figure out the timing of their pregnancy, whether or not it's their old partner or their new one. Also there are many people that go their whole life without knowing who their father is. Paternity testing can see if parts of the parent's DNA is present in the child, which would prove the relationship to the child, father or not. (Further explanation in Examples Of DNA Fingerprinting)
Engrafting Bone Marrow
Some people need to have an en-graft (replace) a portion of bone marrow, sometimes from donors or from another part of their body. DNA fingerprinting is used to identify if the donor's donated bone marrow is a right match for the patient. It's also used to monitor the condition of the en-grafted bone marrow, to see if the body is okay with the foreign object or if it's rejecting the donated marrow.