Hum.
Ran into a shiny starly in my Diamond, but a) any attack would kill it in one hit, b) I hadn't even gotten the pokedex yet at that point (Diamond is a PokeRus game)
Pearl got me a (completely unused) shiny geodude
After a long while, Platinum gave me a (also unused) shiny budew
SS is a Pokerus game...
HG... before we finally went to Mr. Pokemon, shiny sentret, shiny rattata (we took photos, so we know that our starter was on levels 29 and 38 respectively. We IceFangKO'd them in respect); later, whilst looking for a growlithe, shiny pidgey (who is awesome); later still a shiny pinsir in the Bug Catching contest. He nearly gave us a heart attack, I swear, but we got him (and is awesome too, but in a different way).
And then there's my Nuzlocke Diamond (my only GenIV one), in which, somehow, in under a period of fourty eight hours, we ran into two wurmple and a bidoof (and now I have three dustox in that game. And a shiny bibarel.)
(shinies are everywhere for me recently- that's five for me in the last week [only listed gen IV shinies, though])
Never chained one, never got a Reset'ed, never hatched one.