My first shiny was a Staravia in Diamond. It's a Staraptor now. It has a dumb name that was basically my reaction to finding a shiny for the first time.
My first shiny was ghastly in pearl cause I chained it.. I never was lucky enough to randomly run into a shiny (despite playing since fire red/leaf green) T.T
My first ever one in the wild was a shiny Vulpix on my OR cartridge that I evolved into Ninetales. Shortly after, like the next day, I found a shiny Littwick, but I traded it for a different shiny Pokemon. I forgot it's name but it's a gen 5 poke.
My first natural shiny was a Gothorita in X. I've been playing since gen 1 came out in America in too. I don't count the forced Red Gyrados in Gen 2 though.
Mine was a Swablu, but only because I decided to shiny hunt it, using two 3DS' in ORAS with the chaining and horde method took me 3 whole days. Now I only focus on breeding shinies... much easier
Mine was Snover in Diamond back in 2007. I actually didn't know what shinies where at the time, but I still caught it because I thought it was special, about a week later I found out about shinies online, I had to have more.
So several year later, after many random encounters, hatched eggs,events,resets, and trades I have 3 boxes full of many shiny Pok?mon I really wanted, still a few more I'd like to get, but I'm still slowly but surely working on it.