Whether or not I believe in the end of the World depends on who is asking, because I have two answers. If we are having a religious discussion, then the answer is yes. Being a Christian, I believe in the Rapture and Tribulation, but then I would not exactly be around for the end of the world if that occurred. Assuming I am wrong, and as I think most people would see it, approaching the End of the World from a purely logical or scientific point of view, then I would say no.
Based on my first answer, my view is Apocalypticism. An outside force, God, will bring about judgment of the Earth and eventually remake it, but the earth will be destroyed nonetheless. One could argue that end of the world described in Revelations is allegorical, and that the end of the world is some sort of social revolution or climate destruction that forces such, but that would take on a Millennialism view. But speaking of Millennialism, the Rapture and Tribulation could also as Christian Dispensationalism, but I would disagree as it is all the Christians are taken and then the world is destroyed, not necessarily that everyone non-Christian affected by it and Christians are not.
My second answer to whether I believe in the End of the World is no because of statistics and order of magnitude. In recent history, nothing has really truly threatened mankind’s existence and I feel the likelihood of something doing so is small. Statistically speaking, an extinction level meteorite strike is not likely, and I doubt the ability of humans to significantly alter the climate of the earth so much as to make it uninhabitable. Even nuclear winter would not exactly spell the end as humans love to adapt and survive. I do not really consider social revolution to be an “End” so I would discount form of social upheaval.