If the world doesn’t end today (December 21, 2012) at the conclusion of the 5,125-year cycle of the Mayan calendar, then we should look to make the next prediction of the complete annihilation of the human race.
It’s unlikely that a nuclear war, no matter how big, will kill everyone on Earth. So we pretty much have to wait for an alien invasion or an asteroid of epic dimensions. It’s hard to predict those events, however, so let us settle on the one thing we CAN predict.
In about 3 billion years (4 billion if we’re lucky), the Andromeda galaxy will collide with our Milky Way galaxy. This will not be something that we can ride out in our basement. Here is the video of the simulation of this collision:
Don’t pack your bags yet, but perhaps in a couple billion years, we should start thinking about making a long trip to Centaurus A which is about 13 million light years away. It does have supermassive blackhole at its center, so in 4 billion years, that might cause issues as well.