Once we've exhausted the planet's energy resources, we're going to need to move into space to collect energy directly from the sun. We'll build larger and larger solar arrays until we enclose the entire sun in a cloud of solar satellites and make use of 100% of the sun's energy. This "cloud" is known as a Dyson sphere.
In 1960, physicist Freeman Dyson performed a thought experiment. He assumed that the power needs for civilizations never stops increasing. He theorized that if future civilization could enclose our star in a rigid shell, we could generate 384 yottawatts (384 x 10^24 watts) of energy.
There are many problems with the concept. A solid sphere would be nearly impossible to keep suspended around the star without a collision. Plus, even if we used all of the material in the solar system, we would only be able to create a shell 15 cm thick -- not nearly thick enough to keep the shell from imploding. One fix is to scrap the sphere idea for a cloud or ring.