Benefits of space exploration--here's a short list:
Microcomputer technology (necessity due to limited cabin space on lunar vehicles), Sped up development of smaller as well as faster computers for scientific, business and personal use.
Brain/body imaging/scanning technology. How else are you going to monitor your astronauts' heart rates, body temps, etc. from 240,000 mi away?
Age of the universe. Has now been traced back to within microseconds of "Big Bang."
Finding out what would be needed for humans to be able to live in space for months/years, esp. in zero and low-gee environments.
Robert Heinlein wrote an excellent article on this subject called "Spinoffs." It was originally published by OMNI magazine and appears in his Expanded Universe collection.
"Earth is the cradle of Humanity. But one cannot live in a cradle forever."--Konstantin Tsiolkovsky