Three related reasons: Sputnik angst, there was a race with the Soviet Union in every field, and areospace technology development for military purposes.

But the fact is, the Apollo program was a one-shot thing. It was wound down and the US lost its ability to fly to the moon. It also discontinued its high-payload rockets in favour of the Space Shuttle, so now the rocket market is occupied by the European Ariane and the Russian Proton.

The Soviet manned space program made more scientific and technical sense than the American one, and the ISS owes more to the Russian Soyuz and Mir than to the American Skylab, which was also discontinued and folded into the Shuttle.

We have met the enemy, and he is us — Pogo

(1) Spend money on chip research for what? What would the chips be used for? The great proliferation of electronics came on the back of very advanced requirements for components for space programs, etc. One could argue that only once they had been developed for such purposes were it possible to consider their use for more mundane matters. The personal computer only became possible with a maturation of integrated circuit technology, computation infrastructure, and computational techniques that allowed for cheap mass manufacture. The driver for this technology were expensive research programmes in fields requiring processing of large data sets, such as say high energy physics research. Forget about the direct spinoffs, I would argue that the influences of these expensive programmes are far more subtile.  Technological diffusion requires that the basic building blocks are already lying about looking for a different application. You don't start developing processor technology because you think that in 20 years you'll be able to make a machine to play games on.

(2) Missile programmes you say? Because military programmes with large destructive potential are soooo useful while high energy physics, space exploration and the like are vanity projects! And you know how the military loves to share the technology it develops and would not like to keep it secret. One of the great advantages of the large lab high energy physics environment is exactly that it is not a military programme. We don't build things to kill people, I think this is a plus. Further, there is not a tendency to keep progress secret. Quite the opposite in fact, thus a greater chance that progress made here can defuse faster and wider.

(Disclosure, I work at CERN.)