I think my first true shiny Pokémon ever (not counting the shiny Gyarados in the Lake of Rage) was a shiny Magby I hatched from the Odd Egg you get from the Day-Care man in Crystal version. I knew there was a good chance of it being shiny, but looking it up now there's only a 14% chance of the baby Pokémon inside being shiny, so I guess I lucked out a little bit.
In Generation 3 I believe my first shiny Pokémon was a Tentacool in Sapphire version. That Sapphire version is where I found many other shiny Pokémon as well (I don't recall the exact number, but it's above 4), including another shiny Tentacool. In Generation 4 I think my first shiny was a Geodude, though I can't recall. In Generation 5 my first shiny Pokémon was, oddly enough, also my first ever non-Event shiny Legendary Pokémon: Landorus. And just last night I caught my second shiny Pokémon of Generation 5: Absol (with a 31 IV in Attack). Overall, my luck with shiny Pokémon has fluctuated between games: low in the 2nd Generation, very high in the 3rd, medium in the 4th, and now low/medium in the 5th.