I'm not sure if this is technically an organ transplant - it's certainly not one of the cases that one usually thinks of - but Mark Cahill recently received the UK's first hand transplant.
The BBC article includes a useful history of organ transplants (cornea 1905; kidney 1954; heart 1967; hand 1998). It does, however, make the slightly odd claim that "Hand transplants raise more ethical questions than other transplants, such as the heart, as they improve the quality of life rather than saving a life".
This is puzzling because, while many transplants do save (i.e. prolong) lives, many simply improve the quality of the recipient's life, for instance a kidney transplant spares someone having to undergo dialysis. In this recent example (which I already linked to here) a donor is said to help four people but, as Norfolk coroner William Armstrong is quoted as saying in the article, "One life has been saved and the quality of three other lives have been immeasurably enhanced". Mr Savory's heart saved the life of someone who might otherwise have died, but his lungs and kidneys 'merely' improved the quality of life of three people not it seems in immediate risk of death. This still seems a very worthwhile achievement and not to raise particular ethical questions.
One feature of hand transplants - like face transplants but unlike internal organs such as kidneys - is their visibility, as illustrated by the case of Clint Hallam, who received the world's first hand transplant (pictured at the end of the BBC article). In his case it seems that while he hasn't physically rejected the transplant, he has psychologically: he feels that the hand isn't really part of him. This is a particular danger, it seems, for external transplants and something that may raise distinctive ethical questions.