The excitement about cloning started when Scottish scientists at the Roslin Institute successfully cloned a sheep, and named the clone "Dolly". Since then, whatever works that the human imagination and access to resources can come up with have been flooding the airwaves, the movie screens, and the literature of every genre.
One hilarious consequence of the human imagination was the Michael Keaton film, where an overworked man decides to clone himself in order to have some help. The humor comes from the ridiculous notion that a form of human "xerox" machine could be built that would allow clones to pop out, fully grown, and start barging around...
More serious consequences of the human imagination concerned the lack of limits placed on using the very material of life, and what horrors could come from it. Would there be suffering, agonized piles of human flesh built just for slavery, to serve as tissue supplies, or as subjects of horrific experiments as described in Frank Herbert's "Dune" series?
Of course, there are religious reactions to the issue of cloning. Just when the most politically powerful religions become more warped concerning the "rules" about what is divine, sacred, allowed or prohibited, science just has to come along with something that breaks through the walls of "oh hell no!" and forces everyone to scramble for a way to put some controls on frankenscience while fostering the work of progressive science.
It is not difficult to accept the two types of cloning that do not involve producing an exact twin of an existing person, or reproductive cloning.
Recombinant DNA technology, or DNA cloning, works at the fragmentary, gene, or cellular level. There are controversies here, as this technology is used to create "super bugs" which are capable of causing vast damage. But new bacteria which can help to dissolve oil spills, or enhance soils management technologies are beneficial.
Therapeutic technology offers the most hope and promise. But the forms which use the earliest forms of a complete human being are creating religious havoc, especially when people consider human life to start with the fertilized egg. Anything that comes afterwards is a human being, and any use of the fertilized egg, embryo, or fetus is too horrific to comprehend. Others have varying ideas as to where they would draw the line, but still want the cure for their own Alzheimers, Parkinsons and other terrible diseases that are killing people who are considered to be ever so vital to the enhancement of human life.
Reproductive technology is very unsuccessful at this stage. The products of reproductive cloning end up with so many immune disorders, or debilitating and deadly problems that even animal cloning is not a sure bet. Human cloning is a long way off, and would probably be outlawed, as only the exceedingly rich would be able to afford the service.
In summary, there is not just one type of cloning. There is not just one purpose for cloning. There are legitimate religious, legal, psychological, and social issues and concerns about cloning, as this is a world were all humans have to live with the benefits as well as the consequences of scientific discovery.