The very first shiny Pokemon I ever found (that I noticed) was a shiny Magikarp while Feebas hunting in Emerald (I've been a fan of Pokemon since Red/Blue, so throughout the hundreds of hours I've put into Pokemon games since Gold/Silver, that was only the first one
) . Somehow I just knew at the start of the hunt I'd just HAVE to find my first shiny of some sort, and hundreds of water-Pokemon later, I found one! (Then a couple days later that stupid Feebas...)
The next one actually wasn't too far from then, a couple months later when I found a shiny Onix on Victory Road in Platnum while training for the elite four. It was a nice surprise, as I needed something to motivate me to continue training, and it was it!
The last and most recent one was in Leafgreen about six months later. On Four Island, right after entering that ice cave, I was walking around, and got into a battle. As the screen was flashing and going black, I was thinking "Ugh, forgot to put on a repel... I'll definently put one on after this ba..." *sparklesparkle* "What the...?! A shiny Zubat?!" So yeah, I didn't put on another repel for a long time, because if I had remembered, I never would have gotten the Zubat! XD
So far, I have never failed to catch a shiny Pokemon, and all of those three I've found so far are for now at the same levels I caught them at, untouched, until I decide what I want to do with them.