Much is made by theologians, apologists and philosophers by morality, and various moral arguments – some attempting to demonstrate the reality of God, some for other reasons. The Christian claim generally goes like this:
Objective moral values exist.
If God does not exist, then objective moral values do not exist.
Therefore, God exists.
Pretty simple argument. A few definitions: objective moral values = things like murder is wrong in an absolute, objective way – it is true whether or not anyone believes it to be. It *is* wrong – not just determined by societal values or cultural values, but objectively wrong.
There are differing views on this line of argument (there are some pretty interesting takes on the argument, but this is pretty much the core of it). Firstly, is there such a thing as objective moral values, and, if there are, can the leap to God be made so quickly? Many would claim that no such OMV exist. Morality is simply a product of society, evolving with society.
Others would argue that a kind of natural law exists – that there are natural moral laws, such as don’t kill, etc. Most of the time these are grounded in some kind of theism, and most Christians would take this line. Folks like C.S. Lewis argued quite powerfully about the reality of the natural moral law. Aquinas was a key figure in the development of natural law ethics – the gist of his thought was that we could grasp the natural law by human reason apart from faith.
Not all theists agree with natural law ethics, however. Bonhoeffer, for example, denied that there exist natural moral laws that we can know apart from faith. This puts him quite apart from the Aquinas tradition.
There have been a lot of attempts to ground morality in something other than God, some good, some not so good.