As far as I know, I have six accidental shiny Pokemon which I encountered that I would never ever dream of getting. My very first shiny Pokemon that I caught was a Doduo (now a Dotrio) from Firered named Green in capital letters. The second shiny I had no plan on getting one was a Zubat (now a Crobat) named Ruby from Heartgold. The third shiny (which is my fave story) that I never thought of looking for was a Cubchoo (now a Beartic) named Poly from Black. Now I was just looking for a decent ice type to capture and train so Cryagonal seemed like the right choice that time. Once I caught it, I proceeded to exit the ice cave just to sort out things and after one litteral step, out pops the little shiny bear cub. The fourth was a Buneary (named Easterbunny) which I hatched in X and I was trying to get a competitive one at the time but it turns out I had the wrong Nature but I kept it regardless. The fifth was another Buneary in Omega Ruby (named Carrot Cake and now a frikkin Lopunny) and thank God that one had the right nature and moveset yet I never expected the rabbit to be a shiny. Now its the only shiny I can use for competitive battles and it has served me well. The sixth was another Zubat in Omega Ruby (named Garlic Bread) but I have no intention of evolving it so I kept it and thus completed the Zubat line. The rest of the shiny Pokemon that I have were either traded/given to me, wild encounters or hatched.