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Shiny Tentacool popped up one day in Gold when I went surfing. I had no idea what was going on, but the prominent sparkle animation made me decide to catch it just to be sure. Not sure if I still have it anymore, would only be if I transferred it to Stadium 2 and kept it there, but I haven't checked that game in a long time.
Wouldn't see another random shiny until an Unown in Platinum.
I apparently also got a shiny Nidoran-f in a LeafGreen re-playthrough and didn't even realize it until I noticed the red star in Bank after I had transferred it up several generations. Scary to think about how many shinies I may have run from just because I wasn't paying attention.
Other than that, I really haven't seen any others. I don't really hunt for them, I just enjoy them if they pop up.