I got some shinies right from 2nd gen. In 3rd gen, I got a shiny Taillow, Sandshrew, Zubat, Dodrio and Zigzagoon. Got one wild shiny Geodude explode in my face. Encountered a shiny Meoth, Glalie and Bagon in the Battle Frontier.
From 4th gen onwards, I've never found a shiny, not even when I tried chaining some pokémon. I guess it's to conpensate the unreasonable luck (and bad luck) I got in previous gens. :/