Well, events and forced finding notwithstanding. I don't really count such things as chaining or breeding for them as I don't really find that, I dunno, natural? Though I have gotten a lovely little male vulpix I named Shining!!!(you have to pronounce the exclamation marks when you call him) and a pretty little female chartreuse octillery with those methods.
Just stumbling on them in the wild is pretty rare, though as I've played most every generation I have my luck & my stories. My first was a bluenosed Diglett that caught me by surprise in the Diglett tunnels outside Vermillion, so that had to have been the revist gens of FireRed or LeafGreen.
Found a male doduo south of Blackthorn city, but I'm doubting as to whether they even show up there, so I could be remembering that wrong. The Doduo line is my second favorite pokemon species because of Hunter, so named after the shade of green his little balls of feather fluff are!
I've kept my little shiny buddies moving up though the generations with me as often as I could, still have the lot of them with me in my newest X version and hope Moon has some option to too. I suppose event shinies don't count, but I have come to love the gyrados from Lake Rage too. I see him like he was forced to evolve too soon and he's basically a big dumb magikarp trapped in a fifty-foot serpent's body. He wants to be friendly but as he's not used to his body its hard for him to talk without speaking below an ear-bleeding roar. "BLOODRED ONLY WAN FRIIIEEEEEEND!"
Back in Black version, had the good luck for some guy to just randomly trade me a big ol' shiny Snorlax. It doesn't show up too well, but I love my Big Ol' Lardball!
Haven't had much luck since those earlier versions, but recently just outside of Snowbelle city I had the good luck to find a shiny of my favorite grass type, Victrebeel! Named her after what I usually call them, Kusunagi, after the legendary japanese blade that also goes by the name of The Grasscutter. Fitting considering Leaf Blade and the various other plant cutting moves.
Oh, and for those of you with worse luck or still in anticipation for your first shiny, I suggest keeping a couple Quick Balls on you at all times. Rarely have I had one fail me when tossed on the first turn!