In theory it is possible to make clones of living things. For example, some years back scientists managed to clone a ship — they named her Dolly — but she was very unhealthy. Reproducing through cloning can actually increase the chances of diseases and other problems with a person’s development. This is why sexual reproduction is so wide-spread in complex organisms. The only organisms that reproduce by cloning are bacteria and some other simple organisms that are made from only one cell!
As Zena said, if we were to clone a person, there could be problems… the clone would have the same genetic age as the person from which it would be cloned. As you can imagine, that has problems associated with it. Also,the process itself can add further problems or defects to the genome of the clone.
Another issue with cloning humans is ethics: do we have the right to do so even if we could?