I've noticed a lot of people wondering about shiny Pokemon lately, so I've decided to help by compiling this page of Frequently Asked Questions about shinies.

What are the odds of encountering a Shiny Pokemon?
The odds are 1 in 8192, or 0.0122%.

If I breed a Shiny Pokemon, will the resulting Pokemon be Shiny?
The same odds apply for hatched Pokemon as normal wild Pokemon, so the odds of any egg hatching shiny are still 1 in 8192.

If my Shiny Pokemon evolves, will it stay Shiny?

If I clone a Shiny, does it stay Shiny?
Yes. (Thanks to RESIDENT_ZOIDBERG for asking this ^_^)

If I import a Shiny Pokemon to Diamond or Pearl through Pal Park, will it stay Shiny?

Why do I see so many Shiny Legendary Pokemon?
By standing in front of the legendary, saving, and continually instigating a battle against a legendary Pokemon, people will eventually see the Pokemon as shiny. Of course, doing this could take hours, or even days.

Does my Pokemon get any stat boosts or benefits from being Shiny?

I've heard you can find Shinies with the Pokeradar. Is this true?
Yes, you can. When you use the Pokeradar, if you see a spot of grass with silver sparkles emanating from it, it is a Shiny. So get there fast.