My first Amiga was a parental thing. It was when I was 8, and I knew nothing about computers, even though I loved computer and video games. Anyway, my cousins got an Atari console (not the computer, the console) complete with Pitfall, Enduro, Boxing and some Space Attack game. When I saw it, it was 'beg parents until they are insane' time.
They, however, had been thinking about my education, and how I probably needed a computer to type up assignments and so forth. Without me knowing, they went out, shopped around and bought an Amiga 500 with the full 1 meg of RAM and Indiana Jones and the Last Crusade, Kick Off and F-18 Interceptor.
So I was expecting an ad-lib sounding, blocky graphic looking Atari console, but what I got was an Amiga! I admit I didn't know too much about them at the time (no one I knew back then had Miggy's), but when I saw the graphics and listened to the audio, I knew I had something 100x more powerful then my cousin's crappy Atari, and I promptly let them know about this too.
Soon, I met other Miggy users, and we began to copy games for each other and so on...and a wonderful part of my childhood began.