Golden Rattata in Silver... no pokeballs... orz
I knew that time it was rare (common sense, a feeling, instinct... whatever you wanna call it, i suppose)... It was also my first shiny encounter ever.
Second was a shiny Ursaring while finding a Sneasel in Mt. Silver. That one, i did catch. Traded a clone of it (using the box glitch) for my cousin's Blue Nidoking. Those are my most memorable shiny encounters. Rest took years/RNG manipulation to get... and it wasn't as exciting anymore.