I am happy to announce a new book published by Yashar, Medicine and Jewish Law volume III edited by Drs. Fred Rosner and Robert Schulman. The topics covered by the respected authors include those that are very timely and of public interest: infertility, genetics, end of life issues, and other miscellaneous topics. See more about the book here, as well as an excerpt chapter: Impact of Medical History on Medical Halachah (PDF) by Edward Reichman, M.D.
What is the position of Jewish law and tradition on the cloning of humans, assuming that it can be done successfully and without defective products? Disagreement.
R. J. David Bleich (Judaism and Healing, 2002 edition, pp. 146-147) refers to cloning a child afflicted with leukemia in order to obtain bone marrow as "moral and even laudatory." He states the same about cloning in order to find a cure for a disease from which people are currently suffering, assuming that the cloning is "scientifically prudent and undertaken with appropriate safeguards."
Furthermore, "although the cloning of human beings is highly problematic, the cloning of tissues and organs for therapeutic purposes is entirely salutary."
In Medicine and Jewish Law volume 3, Dr. Abraham S. Abraham quotes R. Yosef Shalom Elyashiv as telling him that "the creation of a new species of 'man' without the mating of man and woman [i.e. cloning] is forbidden... [C]loning of tissues or organs is permitted if done for the benefit of mankind" (p. 87).
As posted in a previous post, R. Michael J. Broyde (Voices Across Boundaries 1:2 pp. 31-34) argues in favor of cloning.