I've received a metric tonne of shinies on the GTS (especially in the DP era), but I traded them all off for dex data, because they mean nothing to me.
My first shiny encounter was a Poochyena on Sapphire in 2005. Of course, it was in that part of the game where you can't catch anything.
Then a seven year dry spell (in which my brother encountered 5 different shinies across 3 games). Last July I caught Mini, a Naughty Mincinno on Route 9 (love!), and thank god she had Technician.
In January I was EV training a Diglett on Route 19 and encountered a shiny Blue-Striped Basculin, (had an ok nature, shitty IVs, EV trained anyway). Nicknamed her 'Pearl'. The specialness was diminished, I think, because of the Shiny Charm (also I hate Basculin).
And then, earlier THIS month, I was hatching eggs around Striaton City, and saw a rippling water spot. Surfed to it...
And whaddaya know: Shiny Red Striped Basculin (it was a new save so I didn't have the Shiny Charm). Nicknamed her 'Diamond'. Much better IVs and nature, but I'm not EV training her.