Phil Plait, over at Bad Astronomy has a short note about a friend whose life was saved by science. (Ok, the technologies that scientific discovery enabled.)
My own story goes back quite a few years, to my childhood. I had a severe case of pneumonia. Two major contributors to the fact that I'm still around to blog at you were penicillin and the oxygen tent. Penicillin's story starts in 1928 with Alexander Fleming. He wasn't looking for it at the time. And it took another 12-15 years before years before other people, including Howard Florey and Earnest Chain (recipients, with Fleming, of the 1945 Nobel prize in Medicine for this work), were able to make enough penicillin for it to be used clinically in any significant amount.
Oxygen, on the other hand, owes its availability not to accidental discovery (plus over a decade of hard work), but to thermodynamics. James Dewar took an interest in liquifying gases, and in general, trying to reach absolute zero. Along the way, he invented the Dewar flask (which the Thermos company started selling, hence the name you probably know). I'm fairly confident he wasn't thinking about medicine. He was doing some interesting science, and learning more about how the universe worked. (Liquid oxygen is magnetic -- he was the first person to know this.) He also invented a way to produce industrial quantities of liquid oxygen. Once you've got that around, you have a chance to discover that, gee, it's a useful treatment to give high concentrations of oxygen to people whose lungs are seriously impaired -- like, say, me with my major pneumonia.
Two different technologies, one discovered by accident, and one not thought of for health. So it goes in science quite often. The ultimate uses can be unpredictable. But it's an awfully good bet that there will be a use down the road.