Hahaha, I'm so lame. I only have a shiny Pidgeot. It is the only shiny I've come across. I caught it when I was roaming around Route 1, after hatching an egg in Pallet Town((I hatch nearly all my eggs in Pallet Town)). So, when leaving Pallet Town to put the newly hatched Pokemon in the PC... Voila!! A level 3, mild-natured shiny Pidgey appeared.
This happened to me in FireRed, by the way. And, if you still don't believe me, I will tell you that I have played 700+ hours on it single-handedly. Don't you think that, knowing how long I've played, at some point, I'd come across a shiny? lol