Most limb and male genitalia transplants are considered unsuccessful. Either they reject, or the patient does not become psychologically used to having the graft. (Typically limb grafts have limited sensation due to nerve damage during surgery (it's inevitable). This also means that the graft may have limited movement.) Both of these reasons add up to the general experience of limb transplantation patients - they all seem to describe a feeling of the limb "not belonging to them".
Generally, transplants that are "visible" have a profound psychological impact upon the patient.
kidney
A heart.
A kidney.
A kidney.
A kidney
A kidney
The first successful organ transplant occurred in 1954, when a man donated one of his kidneys to his twin brother.
Lots of organs have been transplanted . Heart eye liver kidney and the testicles
kidney
Heart, kidneys, lungs, liver, pancreas, corneas, and small intestine are all commonly transplanted. Almost everything can be transplanted, it's whether the transplant is "successful" that's the problem. Brains are never successfully transplanted. Faces are only just successful. Limbs can be but usually are not, since they are not essential for life. It is whether the organ is essential for life that dictates whether it is commonly transplanted or not.
Kidneys
Usually the donor's transplanted organ is not transplanted again - it puts a lot of stress on the organ. And depending on how long the donor recipient has been on immuno-suppression for, some of the other organs may not be used (it can affect the kidneys a lot).