Yes, morality is possible without the existence of G-d, just as different kinds of belief in G-d, i.e. religions, have their own variations in morality. People have to decide for themselves what is moral and what is not, just as religion decides. It is often rather complicated in the real world and in extreme situations, as we can see in moral dilemma problems. Essentially, whatever personal moral values one adopts are an individual choice and whatever moral values a given society or culture adopts are based not only on religion but on common human values and norms of behavior, including justice, fairness, compassion, equity, as well as legal rules and regulations that bind a society or culture together.