My first shiny ever was a Suicune, believe it or not. I'll tell the story 'cause I'm bored...
I was playing my first Silver Version game, and I was right below the lake of rage. I ran into a purple dog Pokemon, and I didn't know what a Shiny was, so I ignored the sparkles. I had nothing but one stinkin' Pokeball left, so I threw it AND ACTUALLY CAUGHT IT. I named it Suicie. After I found out what shinies were, i was really happy ^^.
The other shinies I have, in catching order, are Gyarados (Redragee), Unown (Blue), Ursaring (Silverest), Zigzagoon/Linoone (Redskin), Meowth/Persian (Sparklepaw), another Meowth that didn't evolve yet (Magicpaw), Rayquaza (Chromesky), Golbat/Crobat (Rosewing), and Torchic/Combusken/Blaziken (Redbaron).
Took me almost forever to get all of 'em.
~Ho-Roudon