Shiny Pokémon

Every Pokémon has an alternate coloration, commonly known as a shiny form. Every wild Pokémon you encounter has a 1 in 8,192 chance of being shiny. This does not mean, however, that every 8,192 Pokémon you find in the wild will be shiny, as the chances are still the same regardless of how many Pokémon you've encountered. A shiny will sparkle, make a “shine” noise when it comes into battle, and be a different color than normal. Also, when viewing a shiny Pokémon’s stats screen, it will have a star on the page. Shiny Pokémon were introduced in Gold and Silver Versions and have been in every Pokémon game since then.

Shiny Pokémon are not any stronger than normal Pokémon. Trying to breed a shiny Pokémon for a baby shiny will work, but the normal chance of 1 in 8,192 applies to getting one (unless it's in Gold, Silver, or Crystal - see below). This also applies to breeding normal Pokémon.

You should always carry at least a few Poké Balls and other types of Balls. If you run into a shiny and have no Poké Balls, you would be out of luck. Also, certain moves can make a shiny Pokémon end the battle, including Roar, Whirlwind, Selfdestruct, and Explosion. In the case of a wild Pokémon knowing any of these moves, it is best to use a Master Ball, but if you don’t have one, you better hope to catch it before it ends the battle. Another thing to note is that you should never attack a shiny Pokémon unless it is with Super Fang or False Swipe, as it could accidentally knock it out. Catching Page

Red, Blue, and Yellow

Since these games were for the original Game Boy, which was a monochromatic screen (black and white), there were no shiny Pokémon yet. You can, however catch a Pokémon and trade it to Gold, Silver, or Crystal, and if you're lucky, it might be shiny, due to its hidden stats.

Gold, Silver, and Crystal

In Gold, Silver, and Crystal, it was possible to breed a shiny with another non-shiny Pokémon. If you did this, the chance of hatching a shiny from the egg would increase to 1 in 64. This is because of the way stats were handled in these games.

Ruby, Sapphire, Emerald, FireRed, and LeafGreen

In Ruby, Sapphire, Emerald, FireRed, and LeafGreen, finding a shiny was actually as it was intended, a 1 in 8,192 chance. There are no other ways to increase the chances by breeding, or otherwise, in this generation of Pokémon games.

Diamond, Pearl, Platinum, HeartGold, and SoulSilver

A new addition to shiny Pokémon was put in these games. If you obtain a foreign Pokémon (one that's not in the same language as your Pokémon), you have an increased chance of getting a shiny Pokémon when breeding the foreign Pokémon with a non-foreign Pokémon. This is called the Masuda Method, and the chances are then rasied to 1 in 1,639.
If you chain a long chain (the maximum chance is obtained at a chain of 40) of Pokémon using the Poké Radar in Diamond, Pearl and Platinum, there is an increased chance of finding a shiny in the grass if the grass is shining as well.

Black and White

The Masuda Method is also in Black and White, but instead, the chances are 1 out of 1,366, meaning the chances are much more common.

Black 2 and White 2

The Masuda Method's chances are the same as in Black and White, 1 out of 1,366, but there is an added mechanic in these games. The Shiny Charm, which you can obtain after registering every Pokémon in the National Dex, excluding event legendary Pokémon, allows shiny Pokémon to be a little more common. With the Shiny Charm, the chances normally are raised from 1 in 8,192 to 1 in 2,371, and the Masuda Method's chances are increased to 1 in 1,024, making it well worth it to try to "catch 'em all".

Many people have caught or seen a shiny Pokémon, but some still have yet to encounter one. If you're searching for one, keep it up! You'll find one eventually!

Happy shiny hunting!