Torah Currents has an article by R. Michael J. Broyde about cloning. Here's an excerpt:
While some religious traditions, most notably Roman Catholicism, view all tampering with nature in the reproductive area as wrong, that is by no means true for most religious or ethical traditions, including Judaism... Indeed, one is hard pressed to find a religiously neutral reason why cloning would be intrinsically bad in cases where other means of treating infertility would not work...
Cloning, like artificial insemination and surrogacy when they first appeared, has narcissistic possibilities. In reality, however, it will most frequently be used as a treatment for drastic infertility, and like all forms of of assisted reproductive technologies has its place in one of the central missions of humanity: to make the world a better place for its inhabitants.