Mine was a purple Drowzee in Crystal. I had no idea why it was different colored. I got afraid that it was a game breaking bug like MissingNo and I turned my game off XD
Next was a red Geodude in Sapphire and I passed it up because I didn't want it. Yes, I'm dumb.
Then I found a shiny croagunk in the safari zone in platinum. Naturally, it escaped the pokeball and fled.
I think it was Druddigon in Pokemon X. Weird colored dragon with yellow head. Like a lego of some sort. At first, I was like, "what's wrong with this one?" and was thinking whether to catch it or not, but then again, shiny value. *-*
My first shiny was an Unown. Caught it in the cave in Solaceon town in Platinum I believe. I traded it though, because I hated it, even though it was my first. -_-