Although existentialism is not by necessity nihilistic, nihilism does share a close affinity with existentialism because it depicts human life as ultimately trivial and meaningless. Where it parts company with existentialism, however, is in the level of resulting despair and the conclusion that therefore perhaps the best course of action is suicide.
We can find a good expression of the nihilistic existentialism in work by Dostoyevksy. In The Possessed, his character Kirilov argues that if God does not really exist, then only individual freedom in life is genuinely meaningful. However, he also adds that the most free thing that a person could do would be to end that life rather than live under the control of social systems created by others. Albert Camus explored a the same issue in The Myth of Sisyphus, published in 1942, where he addressed the question: should we commit suicide?
There are two aspects to this position which merit attention: whether the absence of any gods renders human life meaningless and whether that meaninglessness forces us to conclude that suicide is the best course of action. The first aspect is technical and philosophical in nature. The second, though, is much more psychological.
Now, it is certainly true that large numbers of people throughout history and even today have believed that the existence of some divine purpose to the universe is necessary for them to have purpose and meaning in their lives. What that majority believes to be true for themselves is not, however, dispositive for the rest of humanity. Quite a few people have managed to live very purposeful and meaningful lives without any belief in any gods and no one is in a position of authority that would allow them to contradict what those people say about meaning in their lives.
For the same reason, the fact that people have experienced great anguish and despair over the apparent loss of meaning in life when they have doubted the existence of God does not, therefore, mean that everyone who doubts or disbelieves must necessarily go through similar experiences. Indeed, some treat that doubt and disbelief very positively, arguing that it provides a superior basis for living that do faith and religion.
Not all claims that life today is meaningless are entirely dependent upon the assumption that there is no God. There is, in addition, the vision of the postmodern man, the image of the conformist who has become dehumanized and alienated by the nature of modern industrial and consumer society. Political and social conditions have rendered him indifferent and even baffled, causing him to direct his energy towards hedonistic narcissism or simply a resentment that might explode in violent behavior.
This is a nihilism depicts human beings who have become stripped of even the remotest of hope for meaningful lives, leaving only the expectation that existence will be little more than sickness, decay, and disintegration. It must be pointed out here, though, that there are some differences in how the concept meaningful life is being used. Those who insist that a meaningful life depends upon God mean it in the sense of a life that is meaningful from an objective perspective.