No species ever lasts, it is just impossible. They all go extinct. Sometimes there is a sudden event, perhaps an environmental catastrophe or the introduction into the habitat of a new predator or competitor. In the case of humanity, our blame for this type of extinction depends on the degree of responsibility we must accept (perhaps posthumously). We have indeed dealt this fate out to innumerable species already.
The obvious one is war- all species compete with one another in some way, but humanity does seem to have taken this to another level. We are liable not to simple reduce the population to a manageable level in which the magnitude of such warfare will not occur again for some time, but actually overshoot that mark and annihilate ourselves entirely. We have the means to do it, and not the discipline to avoid it. I suspect that the non-occurrence of this scenario will be one of pure luck, we will have no idea just how close we truly come to it, just as we have no idea how close we have come in the past.
The third that I can think of is that of evolution. There cannot be birth without death, and there cannot be a dawn for one species without the eve of another. One way this could occur overlaps with the first, in which our species diverges into two, and one out-competes/feeds on the flesh of the other, perhaps after a long period of separation and then reintroduction. With modern travel capabilities the gradual divergence that had already generated the variety of human races is being reversed as we begin the long process of merging and unification. This comes as a result of our way of life, which as we all know is not sustainable. Either war, overlapping the conditions of the second term of extinction, or a slow (or sudden) decay will end the modern world as we know it, and divergence will become viable again. Because no civilisation could ever stand up to evolutionary time, so assuming collapse can occur soon enough to save ourselves from annihilating ourselves and irradiating the planet, the evolution of the human race and extinction of Homo sapiens sapiens will continue on at its current rate. Which brings us to the second evolutionary outcome: the gradual change of the species. New genes are introduced, old ones are changed, deactivated, duplicated... and spread throughout the population normally. Eventually we would no longer be able to breed with our ancestor (modern man) if any still existed, and we would be a new species. Humanity as we know it will be gone, destroying itself, and no one will even notice, even though there are still people to notice it. Though the future of the human lineage is not necessarily an intelligent, conscious and sapient one, evolution does not mean "better", nor does it adhere to our silly ideas about "progress".
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