I remember catching two shiny pokémon. First one was at the beginning of Silver, just after you get your first 5 pokéballs. I was just happily walking through the forest when all of a sudden a shiny Sentret [http://bulbapedia.bulbagarden.net/wiki/Sentret] pops up. I wasn't all that excited at first, it was just a Sentret, y'know, but when it evolved I pretty much shit bricks at the awesomeness that is pink and purple Furret [http://bulbapedia.bulbagarden.net/wiki/Furret_%28Pok%C3%A9mon%29].
Then there's the shiny Electrike [http://bulbapedia.bulbagarden.net/wiki/Electrike_%28Pok%C3%A9mon%29] that I once caught. I think I was trying to catch Latios/Latias when I ran across it. For whatever reason I decided to evolve into an ugly ass shiny Manectric [http://bulbapedia.bulbagarden.net/wiki/Manectric_%28Pok%C3%A9mon%29], and save after it had evolved, too. Why the fuck did I do that? Electrike's shiny form is so much more awesome.
I've encountered a few more shinies, but those are the only ones I've caught.
Then there's the shiny Electrike [http://bulbapedia.bulbagarden.net/wiki/Electrike_%28Pok%C3%A9mon%29] that I once caught. I think I was trying to catch Latios/Latias when I ran across it. For whatever reason I decided to evolve into an ugly ass shiny Manectric [http://bulbapedia.bulbagarden.net/wiki/Manectric_%28Pok%C3%A9mon%29], and save after it had evolved, too. Why the fuck did I do that? Electrike's shiny form is so much more awesome.
I've encountered a few more shinies, but those are the only ones I've caught.