I'm a multi-day tourer, not a long distance, multi-week tourer, but what got me started:
I grew up in Long Island NY (Freeport), where we all rode our bikes for everything: delivering newspapers, getting to junior high school and to high school until you could drive. One day when we were in 9th grade (13 or 14 years old) one of my friends had come back from a family vacation at Montauk at the eastern end of Long Island and he said "My dad said we drove 100 miles - we should bike that."
So, we did - by strapping sleeping bags to our bikes and heading off on Sunrise Highway aiming east - not a water bottle or map to be found on our 5 speed Schwinn and 3 speed Raleigh bikes.
Much hilarity ensued, but I found I just really liked the part about being on a bike and pedaling for many hours at a time. My friends wanted to stop at every attraction (which we did, and spent all our food money at an outdoor Go-Kart track...) but I just wanted to keep pedaling.