Tycho Brahe's research was state-funded. Kepler used Brahe's research to derive laws of planetary motion. Newton's most important work was largely indebted to the prior discovery of these laws.
http://en.wikipedia.org/wiki/Tycho_Brahe
http://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion

The book Longitude details the prize for developing a chronometer (clock) that could be used determine longitude at sea.
http://en.wikipedia.org/wiki/John_Harrison

The Internet exists because of DARPA investment. The original name was "ARPANET."
http://www.livinginternet.com/i/ii_arpanet.htm
(I used to work for BBN, btw.)

A HUGE amount of scientific advancement was achieved by government investment to develop instruments of war.

There are other reasons for doing this. We used to have political leaders who understand it.
http://www.youtube.com/watch?v=FYb_mhiE-qU