This is another thing people believe simply because they trust in the Bible. This is a future event, so obviously, there can be no evidence that it has occurred. The major pieces of evidence that it will occur are the recorded promises of Jesus and the Revelation of John. If you believe everything leading up to those, and believe that this could happen, then you really have no good reason to believe that it won't happen. I've already indicated that I believe this will happen and explained a bit about how I think things will be after that. Let's discuss what will happen just before Jesus comes again.
Now, I don't know that anybody's really got this right, including me. The details of the actual process are tied up in visions full of symbols that have been interpreted in a host of ways. Churches have split over some of these interpretations. I'm sure you can make your own exhaustive survey of the topic. So, there are only two things I'm sure of. First, it will happen. God's plan for the universe will be fulfilled. If God's doesn't have enough control to ensure that, then he's not really God. Second, no one knows exactly when. No one. Anyone who claims this knowledge is deluded, lying, or completely mistaken, much like many people think Jesus was. Alright, they may accidentally be correct, but the Bible makes it clear that this knowledge is not available to mere mortals. In fact, in one strongly Trinitarian account, this was not even revealed by the Father to Jesus! It can be safely said that every doomsayer up until now has been wrong, and I don't believe the current crop is any smarter. Hal Lindsey has been wrong for a long time. Many people were fairly convinced that Y2K was going to be the start of something big. Drs. Dobson and Kennedy were both ringing those alarms, and Jack Van Impe is still doing it. We all know now what didn't happen at the turn of the millennium. I know that most of these people have the best of intentions, but they're still wrong, and every wrong guess has the same effect as a deliberate lie. People stop taking the warnings seriously.
On the other hand, even if we don't know exactly when, that doesn't mean we don't have any indicators at all. I have to admit that some of those indicators are much more likely to be fulfilled in the very near future than at any previous time. These indicators concern the establishment of a global government, economy, and religion. I don't think that any of those were remotely possible without the transportation and communication advances of the last half-century, maybe even the last decade. We already have the start of a global government (the UN), with its own "peacekeeping" force. Economic unions and the Internet are breaking down national borders in the cause of global trade. And now, the UN is hosting a conference bringing together leaders from many different faiths in hopes of bringing about some agreement concerning mutual religious tolerance. One of the key speakers was Ted Turner, who forcefully stated that, "We are all one race, and there is only one God that manifests himself in different ways". This summit is related to a movement called the United Religions Initiative. It's intended to be a "global community" dedicated to promoting interfaith cooperation. So, there are inklings of things that couldn't have happened before, but could happen within a generation. There have always been reasons to think the time was short ("wars and rumors of wars", "famines and earthquakes in many places"), but there may be more reasons now.