I caught a shiny pikachu in Ruby and a shiny exeggcute in leaf green.
I caught the pikachu without even noticing it was shiny, It just appeared while I was at the safari zone, I threw the ball and caught it. Two days later I was looking at my pkmn's nature, and I saw the shiny symbol on pikachu, I remember jumping out of the chair.
With the exeggcute, I was at the safari zone (again) and the first pokemon that showed up was that one, I kept on throwing food and rocks to the thing so it wouldn't escape. I threw two rocks in a row and then a ball, eventually I caught it and evolved it to exeggcutor, I still have it in my team