I caught a shiny Psyduck in the Diamond Safari Zone. I nearly **** bricks when I saw it, but thankfully I managed to snag it! I then traded it for a shiny Starly, because shiny Golduck is ugly as hell. >: Shiny Staraptor, on the other hand, is badass <3
Over the course of my Pokemon career, I've had a shiny Togepi (lol the Togepi that hatches from the egg you get in Gold/Silver was shiny for me), shiny Smoochum (that other egg that you get in Gold/Silver, no joke), shiny Raltz (it was a boy, and it was modest, so...well now he's a pretty shiny Gardevoir), shiny Zubat, shiny Doduo, and shiny Eevee. I still haven't touched that Eevee. I know I wanna make him an Umbreon (he has a good nature for it), but he feels too precious to touch, haha.
I've also seen a shiny Meowth on Gold/Silver, but I was young and naive back then and didn't obsessively carry over 100 Pokeballs with me at all times, so I had nothing to catch it with. I ran away from it because I felt too bad murdering it...