Excluding the obvious Gyarados and assorted events (Pichu, legendary beasts...):
- Onix (Platinum) - Magikarp (Platinum) - Slugma (LeafGreen) - Mareep (HeartGold) --- "Many of you feel bad for this lamp...That is because you're crazy. It has no feelings! And the new one is much better." (IKEA's Lamp commercial)
I've returned to Pokemon since the Yellow/Gold days with Pearl onwards, and I've convinced myself I'd never capture a shiny, like, EVER (and no, I'm not counting on those that were given away by events)...until Platinum came out, and randomly found a Onix merely because I was training inside a cave.
The rest, well...I've found/caught them also by sheer luck while doing random stuff.
Really, great things can happen when you least expect them to. --- "Many of you feel bad for this lamp...That is because you're crazy. It has no feelings! And the new one is much better." (IKEA's Lamp commercial)
I caught a shiny Tentacool in my first ever playthrough of Silver way back when. Back then I had no idea about shinies but I knew what I'd come across was rare obviously, though I did at the time think it was more powerful than a normal Tentacool so I instantly put it in my team.
I've also had my Pokemon infected with Pokerus before too during my first playthrough of Black. Good times. :) --- incest is wincest - blackmage069 3DS Friend Code: 4768-7429-0881
My prized one is the Shiny Rayquaza I caught several years ago through RNG abuse. I've had it ever since... --- Every wound a new opportunity, every curse a new challenge. I shall encounter defeats... But I will not be defeated.