Beginning around 5 billion years from now, the Sun will expand, becoming a swollen star called a red giant. By 7.5 billion years in the future, its surface will be past where the Earth's orbit is now, consuming the Earth.
In 500 million years the tectonic plate movement and geological activity on planet Earth will have stopped, causing it to have a similar fate to Mars. The planet will be dry, lifeless and very cold.
Within half a million years it is extremely likely that the Yellowstone supervolcano will erupt, wiping out life in several nearby states and causing an environmental catastrophe worldwide. However, we are already due for an eruption, and the underground volcano has shown increased activity over the last 30 years. This is a disaster of enormous scale waiting to happen; we just don't know when it will happen. Fortunately people are looking for ways to relieve some of the pressure that is building up beneath the National Park.
Within 100 years we will be almost completely out of fossil fuels, so we will have to rely on other energy sources. The last remaining fossil fuel will be coal, which is estimated to be gone by the year 2150.
Within 50 years machine intelligence will surpass that of all humans combined. This event has been dubbed "the singularity", and it will forever change our fate. From that moment on machines will make most of the technological advances, and possibly at an ever accelerating rate. Over time humans will become more integrated with technology, and we will no longer be purely biological.