Golbat in Silver Version's Ice Path. I didn't know that Pokémon besides the Red Gyarados could be Shiny and didn't notice a color difference due to the poor lighting, so I figured the sparkle animation was just my eyes playing tricks on me. I tried to run, but I couldn't. Rather than "Couldn't get away!" I could've sworn it said "You don't want to do that!" I ended up catching it, later noticing the triple-star symbol on its status screen.
I told an older cousin of mine about it later and he taught me what and how rare Shiny Pokémon were, as well as how jealous he was having never found one himself.
I eventually evolved it into a pink Crobat. (I was not a fan of what they did with Crobat's teeth in Pokémon Stadium 2. So freaky!)
Sadly, I think I ended up killing it by corrupting my file with GameShark codes. I would've lost it anyway when my battery ran dry, but still...