Sergei Prokofiev: Violin Concerto No. 1. I could expound on other bits of Prokofiev (I still can't believe he wasn't in my Desert Island Discs from a few months back...), but this is responsible for a lot of things.
My father (there he is again) had - probably still has - a recording of this by David Oistrakh. One day, he was listening to it while my sister and I (probably just me, in truth) zoomed annoyingly around, pretending to play the violin in an exaggerated and, well, annoying fashion. Dad was patient, but said something to the effect that one day, we would understand. The implication that I didn't understand prompted me, some time later, to try. I taped the whole LP - the other side was the Cinderella Suite - and listened to it from time to time.
Then I got a summer job, driving a delivery van for a firm specialising in underwater surveying (they appear to be called Fugro-UDI these days) and I spent several summers hurtling aroung Aberdeen with various bits of high tech equipment rattling around in the back of my van. After a few weeks of listening to the somewhat substandard radio, my coworker and I rigged up a tape player, and I stuffed the Prokofiev in. Admittedly, I couldn't actually hear the quieter passages, but those I could hear began to make sense to me - I started picking out themes, understanding structures, appreciating developments, and so on. I came to know it quite well - except for the quiet bits - and can, to this day, be heard whistling bits of it in unguarded moments. It was my first real experience of getting to know a classcal piece properly, and it changed the way I listen to music. And every time I hear it, it's July 1982 and I'm speeding down the hill to Bristow Helicopters' goods in, hoping I haven't missed the flight.