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I've only seen and caught three Shinys in the many years I've been playin' Pokemon, all caught in Mt. Silver in SoulSilver.
Two Shiny Onixs, male and female. The male had a shit nature, so I just traded him to a friend to evolve a Magmar to Magmotar. But the female, named Jasmine after the GL, has a Impish nature, benefiting the stats that matter, so I evolved her into a Steelix. Not to mention that its Ability is Rock Head, so I taught her Double-Edge. Man, that shit is overkill.
The only other one I've caught is a Shiny Ursaring named Hulk. Its nature is Brave and Ability is Quick Feet, which is a good combo. And just like his namesake, Hulk can wreak your shit up with Thrash and Outrage.