In my review of Sagan's Demon Haunted World, I mentioned my favorite chapter was on the short-sightedness of asking "What's the benefit?" from scientific investigations. The answer is "We don't know, but they're huge." Sagan discussed Maxwell's tinkering with E&M leading to everything from toasters to TVs.
Most people can at least see that connection, but in Astronomy, connections are often more difficult to point out. Astronomy is a prime tool for testing basic physics, which can then, in turn, be applied to all sorts of things, but that's a logic train most people can't quite follow.
But recently, Discovery News had a cool article about how research looking at spectroscopy in stars, may be turned to medical applications.