There are religious people who claim that there can be no morality without religions. On the other hand, many scientists have clearly demonstrated that all humans really have an innate feeling for right and wrong. However, I think that these Christians are right in a way. There is name a clear-cut difference between religious morality and more universal human concepts of right and wrong.
For example, killing people can be a quite moral thing to do according to the Christian morality. It just must be done when it is sanctioned by authorities in a war or as a punishment for crimes. The innate human feeling of right or wrong has, however, more to do with the feeling of fairness or justice. We quite naturally see what actions are fair or just and what are not.

Of course, also this ability is more well developed in others. It is less well developed in some others, as are all other human abilities too. Sociopaths and psychopaths often suffer from a complete lack of this important facility. It is, of course, the central reason for their antisocial behavior in the first place.
The most natural basis for human behavior is the Golden Rule or the idea that you should treat other people as you want them to treat you. This idea is present in all cultures. It is by no way a product of Christianity, even if many Christians are fond of making such claims.

This very basic idea is, however, present in many older religions and philosophies. It is a quite natural thing for all creature that lives in herds like humans are. However, the Christian writers who write against the existence of a universal feeling of justice like to bring up the well known studies where subject were asked to give 'electric shocks' to actors as punishment for failing different tests in a laboratory.
In these studies subjects were universally willing to give shocks that were told to be of a very dangerous level. These Christians do claim that this shows that we do not have an inner sense of morality. According to them we are willing to subject people we do not know to severe punishments, which they do not really deserve.

The critical part here is that the order to electrocute people came from people in position of strong authority in the given situation. The example does just show how willing most people are to subject themselves to the authority.
Unfortunately this willingness to succumb to authority is so strong that it overrides our inner sense of fairness. This is the very point where also religions do come to play.

Le Moulin de la Galette, Pierre-Auguste Renoir 1876 - Wikipedia

In fact, what many religious people mean be morality is very often just following of established social rules that are hold by the majority of people. There is no inner sense of right or wrong that would say that, for example, masturbation is wrong and even a grave sin and an affront to morality. This is true, even if all Abrahamic religions (Christianity, Islam and Judaism) are so fond of telling people just that for some unfathomable reason.
This happens even if the act of masturbation does not violate the rights of other people in any meaningful way. This kind of sexual morality is not a natural thing for humans at all. It is a culturally evolved trait that is wholly dependent on the current status of society and its needs, but most of all on the currently ruling ideology.

Those who have been in positions of power have generally support Abrahamic religions wholeheartedly. This is because these religions do help to generate automatic and unquestioning subjection to authority. It is in the very core of all of these faiths.
By this alliance with the forces of authority in society religions are indeed a major source of morality in societies. However, this kind of morality has little to do with the ideas of fairness or even justice. It has very much to do with blindly obeying the current uniform social norms of the society.

We can very easily determine by ourselves what is right or wrong as individuals, but religions are needed to class normal human behavior like premarital sex or masturbation as immoral. However, in the real world we do not need religions to tell people that stealing, giving wrong evidence or killing people is wrong.
There simply cannot exist an stable agricultural or modern society based on private ownership, that would not prohibit those actions. Allowing them would endanger the whole basis of the society.

What many people consider as morality is, however, a set of rules that governs our sexuality. The difficult part of giving up hunting and gathering and taking up agriculture was that humans were now permanently in contact with other humans that were not their family.
Controlling the natural sexual urges was much less of an issue when people were wandering in small groups in forests or savanna. However, it soon became a major issue in agricultural villages.

There soon emerged a set of rules to harness the sexual urges that were seen as a disruptive forces. These rules were given an air of extra authority by incorporating them in the very core of the new emerging religions of the settled agricultural people.
The new need to control ownership and most of all inheritance was the other major factor in the emergence of these new social rules controlling all aspects of human sexuality.

A major problem, however, is that these rules are still all too often applied to a quite different postindustrial society. The needs of society have been revolutionized, and we have the means to control human reproduction are freely available.
This heavy control of sexuality is not innate in us at all, but is enforced by religions, even if they are not at all necessary for the well-being of the society anymore. On the contrary, the continuation of the religiously motivated bans on birth control pills and condoms do endanger the whole future of the human kind. These bans are already a major cause of overpopulation in a situation where it is one of the gravest dangers facing mankind.

(This piece was completely rewritten on 11th of September, 2012)