Researching the sun, moon, and planets: - planetary probes like Voyager, Pioneer, Viking and Pathfinder landers on Mars, Magellan probe to Venus, these and others have all changed our entire view of the solar system and all the planets. Nothing else has ever given us the close-up view of the planets or their moons. For example, no telescope could ever have shown us the volcanoes on Jupiter's inner moon Io or the ice on Jupiter's second moon Europa. Nothing could ever have given us the clue that there could be life on those moons, aside from the space probes we've sent.
With these probes and the new, powerful orbiting telescopes we've put in place, we are updating our once-simple view of the solar system - learning about the many asteroids and comets and their complex orbits. We are only now becoming aware that an asteroid or comet may have been the end of the dinosaurs, and could be the end of us. By studying our solar system, knowing what's there and what threatens us, and devising the capability of averting disaster, space exploration could mean the very survival of the human race.
We may care very much some day about this reason for space exploration.
Reason Number 3
Marvin's autograph: well maybe not his, but the more we learn about our solar system and the universe the more likely it is that we'll someday contact intelligent life.
Reason Number 2
Satellites in orbit: The biggie in my opinion - you would not be reading this page if it weren't for communications satellites that make the world wide web possible. Thousands and thousands of lives would be lost each year to hurricanes if it weren't for weather forecasting satellites. Even the war in Iraq would have come out differently (and not in favor of the allies) if it weren't for satellite positioning capabilities. The civilized world owes much of what it is today to satellite technology.