If a person is kidnapped there is a chance that the victim is in great danger. If the ransom is paid, the victim is not guaranteed clear passage home. On the other hand if the ransom isn't paid and there is force there is a chance the victim might be moved or killed in the rescue attempt. It is a tricky thing either way.
Sometimes the only alternative is to pay the ransom. If it is a life or death matter, which kidnapping often is, it is better to pay the ransom than to have the victim die. People should not be sacrificed for the sake of "principles" or to avoid setting a precedent.
Kidnappers typically ask for a ransom as payment for returning the kidnapee. One recent instance is the kidnapping of the mother-in-law of Formula One boss Bernie Ecclestone. The kidnappers demand $36.5 million for her safe return. This ransom should not be repaid because it's just a trick for the kidnappers to get some money - they could care less about the woman's health and safety.
Complying with criminals only further perpetuates the cycle of violence, kidnapping and war mongering that has been going on for years. To give in to the demands of these criminals is only aiding and abetting them to continue to do what they are currently doing, while bankrolling it. There are always other ways of dealing with these types of situations and giving into their ransom demands are not one of them.