I have been riding bicycles since I was 3, dreaming of owning a moped since I was 12... but it wasn't until 1996 when I first became an owner of a motorized bicycle.
Bike Machine is a small 35cc gas motor with a friction drive roller. You mount it on the rear wheel of any bicycle, put a pint of gas into it and off you go! It's loud and gathers looks from anyone in 200 ft radius.
The design is similar to the famous Solex moped, except Solex motor drives front wheel.
I bought it got for $100 from a co-worker and her father helped me install it. After he started the motor with the pull-start, I heard how noisy it is and got scared. My first question was: "How slow can it go?". He gave me a puzzled look and said: "I'd rather find out how fast it can go!". So, he rode it off, I looked and decided that I want to give it a shot too... after all the money has changed hands already.
It was fun and weird at the same time. Eventually I got it going full speed (20mph, but it feels faster than that) and felt the state of "whee!!!" coming over me. I took it home and rode it every chance I got.
In time I discovered a limitation of the friction drive - it hates rain. As soon as the wheel gets wet it starts slipping and if you don't stop the motor, it will eat thru the tire and puncture the tube (yikes!).
Keeping this in mind, I only rode it when forecast was clear.
Another thing I found out is that bicycles are not designed for the kind of vibration that Bike Machine generates - twice I had the frame break and moved the motor to another bicycle (fortunately I had tons, since I was always buying them at garage sales).
Even though I enjoyed it tremendously, I started longing for more speed and better breaks, so I started searching for a moped. My unsatisfied 'moped desire' resulted in me reading all I could about those miracle bikes - I checked every website I could find (there was less than a handful at the time), bought used moped books and read moped newspaper articles from the 70s in the library via microfiche. That was the time when I created my Moped.org site (now Moped2.org).
Bike Machine has not been ridden in many years, but it's still sitting in my parent's basement, waiting for the someone to pull the cord and enjoy the WHEE feeling!
Here is a pic of Bike Machine (no, it's not me in the picture:)