In many "Does God Exist?" debates the question of moral authority comes up. The religious camp claim that without God all morality is subjective and so anything goes. The atheists often say morality is innate. See Hitchens debate here, along with comments.
I side with the religious people here. Morality is subjective. How do I justify this? Well, every act people today consider immoral was at one time deemed praiseworthy or commonplace. Thus we can say that morality changes over time and location. Some religions wear a cheesecloth across their faces when they travel lest they swallow a fly as they consider all life to be sacred. Some people think that killing animals in a kosher or halal way is just and some people find that cruel. And some people hunt animals for sport. These are all activities humans engage in today and consider moral if they live there and immoral if they don't.
So if we can accept that morality is subjective and run with that then where do we end up? Well, we get to the religious argument that without objective morality who are we to say what is right and wrong? Where does morality come from in that case? Let me address that very question.
Humans are a result of evolution by natural selection (even if you don't believe that please try to follow this reasoning) so we must have a certain morality (as we see it) built into us as a way for the species to survive, e.g. even dogs have a sense of fairness that surely must come from them being social animals rather than God. I would imagine that primates have much more complex structures built into their genes and/or brains to enable the species to thrive and as top species in the intelligence league we must be even more developed in many inbuilt social fairness aspects. So we tend to have some sense of justice built in by nature but that changes depending on species, lions kill the young when they take over a pride to ensure the dominance of their genes, humans would never(ish) do such a thing.
Children are then influenced by their parents. They take the morality they were born with and add to it as their parents tell them right from wrong. This is not a moral right/wrong though, this is a survival process. babies that ignore their parents warnings that the green berries are bad will not survive long enough to keep that attitude in the gene pool.
As children age they are then influenced by their peer group. Groups of youths tend to have similar morals. They want to fit in and find it hard to be different, again a survival skill as loners tended to do badly in the mating stakes in pre-history.
Young adults are then hit by the laws, and morals, of society at large. This is what makes countries across the globe so different. There is a personal punishment for breaking these codes of conduct rather than an evolutionary one so the idea of breaking with society tends to be more prevalent. It also allows people to challenge the societies' laws without incurring a reproductive disadvantage.
Once all these moulders of right and wrong have been laid on a person, only then can they apply their intellect to decide on things. If the previous morality has been ingrained deeply then the intellect is not enough to break with that. If they are able to challenge their own morality from a reasonable point of view then they can have an adult view of right and wrong.
Intellect, and the application of it, is what makes society change. We see the action and try to work out if it should be punished, rewarded or ignored based on the results it produces. Hence we see the results of slavery through an empathy with the slave (or a fear of being one) and decide it is wrong. We see two gay people and think "where is the harm?" or think "what if gays were in the majority and decided heterosexuality was illegal?" and give gay couples equal rights.
Society has moved forward, morally, due to people applying their intellect in spite of religion, not because of it. While all of the causes of morality are valid, it is only the intellect that truly makes it right, otherwise we are simple animals. So, subjective as it is, we strive to make it better each generation and move further away from the major religions' versions of morality with each step.
EDIT: To be fair this was my first stab at morality and was a reaction to the certitude of religious people and the smugness that only they have access to a higher morality. Having moved on with my thoughts, it seems that this was a basic stab at personal utilitarianism, but comes across as less subjective than intended. It now seems to me that morality is a personal thing, a collection of principles, values and preferences that were attained as above, but variable over time and weighted differently depending on hunger, tiredness, colour of the room, magnetic fields etc. It is so variable within even a single person over short periods of time that the idea of it being objective is laughable. The argument in favour of utilitarianism requires that it knows our desires better than we know ourselves (possible) but also that it knows our future reactions to having certain preferences met and others not, along with the preferences of those not yet in existence. The idea that we should sacrifice in the here and now for creatures that don't exist is a little too close to religion for me. Utilitarianism fails on many levels, even if we ignore the practical problems of working out what would actually make people happiest and not what they want. There is value in a coarse utilitarianism when it comes to public policy, but it would be better in my opinion if it were to improve the minimum levels of happiness more than increasing the maximum - but that's a subjective opinion because it appeals to one or other of my values...