I've found a shiny Zigzagoon which I caught and have transferred from game to game to this very day.
 
I also managed to breed a shiny Turtwig :D

In the original Pokémon Silver, I saw a Gold Onix. Alas I had no Pokéballs left....
 
Ten years later, in Pokémon Pearl, I caught a shiny Weepinbell... I was just a boy back then...
 
Seriously though, that was about 300 hours of playing Pokémon games in-between shiny Pokémon.

I once saw a blue electrike on ruby, but didn't think anything about it and ran away.

Shiny Nidoran male in FireRed in the Safari Zone once(which is supposedly a bad place to get shinnies), and now I have a blue Nidoking! 

I have a shiny Rattata in SoulSilver, a shiny Eastern Shellos in Diamond, and a shiny Tentacruel in FireRed. Never encountered a really cool one though.

i just caught a shiny poliwag, yay

That thing that evolves into Hypno on the original Gold.

So, less than 24 hours after posting here that I had never seen a shiny, I finally found my first this morning.  
 
 
It was a Magikarp. 
 
 
I was less than amused.

Caught a shiny Wooper in Pearl and also an Eevee through the Global Trade System by sheer luck, I guess.

A  surskit, didn't even realized it until I transferred it on pearl.

I had a shiny zigzagoon on sapphire and a shiny diglet in firered... he had a blue nose.

Gloom, Tentacool, Rattata, Palkia, Charizard, and Bellsprout. All are legit.
 
That shiny Charizard took me about a week to get.

I've got shiny Tentacruel and shiny Budew, I guess i'm lucky since I never went out to specifically look for them.

I have a shiny Linoone, Sneasel, Pichu and Red Gyrados as of now

I remember back in gold version, Ho-oh kept killing me and being a hoarding prude, I forced myself to keep going and going at him without using my one master ball, and using the ultra ball while relying on the up+a+b thing (unsuccessfully).  At one point, I noticed the sparkly animation and realized he was then a different color than I was used to, a gold-ish brown color.  That just caused me to go ".....huh".  I just happened to be successful in catching him on that go around and it was over a year before I learned the significance of what I had done.

I've seen a shiny Zangoose on someone's game once, we were unsuccessful at catching it. :(

caught a shiny fearow in pearl. i still hate fearow