It's a question that I've seen pop up on most OTR sites since the onlines brought me the glory of Newsgroups and alt.radio.oldtime, but I've always found peoples stories fascinating.
I, for one, started when my dad had me listen to all the shows that were emerging from vaults, and aired again back in the 70's. I loved Fibber and Molly, The Shadow, Suspense and the "new OTR" of Radio Mystery Theater. The one joke I have with my Dad is that we both listened to those shows 'back when we were kids'.
As I became a teen, my love of OTR became something I did in secret since I was involved with the punk/hardcore scene, and my friends had a hard time trying to figure what to make of me when they dug through my tapes and came across things called "The Country of the Blind", or "Our Miss Brooks". I'd quickly snatch them away and say I listened to a lot of audio books.
But that seems to have turned around, since I worked downtown a few years ago, and the club on the main floor had a band called "The Mercury Theatre" playing there. I looked them up, and though they're not very good, all their music is based off old radio shows.
http://www.myspace.com/themercurytheatre
I was ahead of my time.