Catechism of the Catholic Church 2296:
Organ transplants are in conformity with the moral law if the physical and psychological dangers and risks to the donor are proportionate to the good sought for the recipient. Organ donation after death is a noble and meritorious act and is to be encouraged as an expression of generous solidarity. It is not morally acceptable if the donor or his proxy has not given explicit consent. Moreover, it is not morally admissible to bring about the disabling mutilation or death of a human being, even in order to delay the death of other persons.
Papers / Essays
Dr. Jay Boyd, Ph.D. and Dr. Paul Byrne, M.D. "May We Donate Our Organs?"
Bps. Fabian Bruskewitz and Robert Vasa. "Are Organ Transplants Ever Morally Licit?" (PDF version)
Judie Brown. "Vatican to "debate" organ transplantation? Brain death?"
St. Louis Catholic blog. "The Hidden Moral Dangers of Organ Donation\"
Monica Seeley. "Not quite dead? The case for caution in the definition of "brain death"
Randy Engel. "Book review: Finis Vitae — Is 'Brain Death' True Death?" Part 1 and Part 2
Dr. Jay Boyd, Ph.D. "Brain Death and Organ Donation"
Dr. Jay Boyd, Ph.D. "May We Donate Organs?"
Peter Baklinski. "She’s very much a living person": Doctor champions 13-yr-old "brain dead" girl on ventilator
Camille Giglio. "Declaring Jahi McMath brain-dead is bad science"
Dr. Paul Byrne, M.D.:
"Catholic teaching on death and organ transplantation"
"Jahi is not truly dead, Wesley Smith"
"Jahi McMath — Accepting Her Life"
"Killing for Organs: When Are We Alive or Dead?"
"The Truth About Organ Donation"
Bp. Robert W. Finn. "Jahi McMath: Sometimes Things Are Not As They Seem"
Brian McCall. "Life or Death in the Brave New World"
David W. Evans, M.D. "Brain Death"
The Truth Behind Organ Donation and Organ Transplants