My first shiny was a Milotic from VGC 2009, so that's not interesting. My next one was a Shiny Drowsee in Heartgold, which I lost due to my DS dying.
I think my most interesting 2 are my Shiny Cottonee and my Shiny Chikorita.
The Shiny Cottonee was kinda funny. I was looking to add one to my team, and thought to myself, "Wouldn't it be cool if I found a shiny Cottonee to use for my team?" Lo and behond, I found one a few encounters later. I sadly do not have it anymore, and I'm not entirely sure why, but I believe my younger self traded it for a shiny Weavile which I DO still have.
The Shiny Chikorita is what I'd consider my luckiest Shiny. I decided to restart Pokemon Soul Silver, and I wanted to try Soft Reseting for a shiny starter. After only around 34 resets, I managed to get myself a Shiny Chikorita, which I used throughout the playthrough. Mind you, this is Gen 4, back before the doubled the shiny rate, and it was without Masuda.