Around the summer of 2006, I found my first Gen III shiny, a Poochyena. I found him on the route west of Lilycove. I was cutting through the route when he appeared, so I had to use a Master Ball (also, he could have used Roar).
About a week later, I was playing FireRed when I bumped into my second Gen III shiny, a Pidgey. It happened after I beat the Elite 4 and darted through the starting route. I caught him using a Master Ball, too.
In October 2006, I found a shiny Lugia at Navel Rock in Emerald. Boy oh boy, did I scream. :P I was soft-resetting for her and I found her within a few days of starting (about 500 soft resets). I was very eager to get shiny Ho-oh, but he took about 11 months. Only within the past few years did I realize that Emerald's RNG was against me - my "shiny frame" only appears 40 seconds after powering on the game. So, since I was soft resetting quickly like mad, that's why I initially didn't find the Ho-oh so soon. I had to wait a few more seconds, darn it all... Lugia is named Angel while Ho-oh is named Demon.
So with RNG, I later got a shiny Kyogre, Rayquaza, and my favorite regi, Regice.