My first ever Shiny was in Pokemon Pearl. I was using Action Replay frequently, so when I saw a random Blue Medicham in Victory Road, My 10 year old mind thought I had broken the game. I named it "Blue", and it's now forever in My Pokemon Ranch, because I had restarted my Pearl version without withdrawing the pokemon from it.
My second shiny was in Pokemon HeartGold. I was going to Pewter City through Viridian Forest when I encountered a Shiny HootHoot. I, to this day, have no idea where it is LOL.
My third shiny is my Shiny Dragonite, Which I had bred using the Masuda Method. It had both the correct Nature and the correct Ability, so I got reaaaally lucky. I named it "Barney" because... well... it fit.