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A bit of a multiheaded question here, but it didn't quite justify being four different questions.

  • Is it possible to get a shiny legendary pokemon in the Pokemon games?
  • If so, when is it generated?
  • Does the overworld sprite reflect the shiny status?
  • Does this vary by generation?
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Yes, it is possible to get a shiny legendary.

For an interactive legendary, the overworld sprite will not reflect the shiny status. It is generated when you initiate the battle, which is why some people save in front of the legendary, battle it, and reset until it's shiny (a process called soft resetting or SRing).

For a roaming Pokemon, the conditions occasionally vary. Typically it's set when you first encounter it and it's registered in your Pokedex.

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This is made much easier in a process called RNG abuse, in which you seed the RNG via time delay from the Continue game screen accompanied by character actions. There's even a program for it. – Corey Jul 9 '10 at 18:43
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The Shiny attribute on a pokemon can generated from anyway you would normally catch a pokemon, egg or in battle. The odds of this are 1 in 8,192 for battles. Some people believe that it must be the first time you encounter that particular species for the first time. There is no evidence to support this.

Starting with 4th generation games, the odds of receiving a shiny pokemon actually increase with the number of battles you're in if you use the PokeRadar. This is known as "chaining." Chaining has been shown to be effective up to chains of 40. You'll know it has worked because the grass will glow instead of shaking.

Additionally, 4th generation games provide for breeding between different nationalities of pokemon. This has been shown to increase the odds to 1 in 2,048 (a significant increase).

If you'd like to know more check out Serebii.

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Doesn't chaining only apply to use of the PokeRadar in Diamond/Pearl/Platinum? – Macha Jul 9 '10 at 17:19
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Diamond/Pearl/Platinum would be the 4th Generation games. I think you do have to use the PokeRadar but I'm not 100% sure. – tzenes Jul 9 '10 at 17:20
Yes, chaining is done with the PokeRadar. – Kevin Y Jul 9 '10 at 17:22
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It's a 1/8192 chance, not 1/8192 battles. People wish it was as easy as 1/8192 battles. – Grace Note♦ Jul 9 '10 at 17:40
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@Grace I think what you are alluding to is that odds do not guarantee success. If you actually engage in 8192 battles with odds of 1 in 8192, you only have a 64% chance of success. – tzenes Jul 9 '10 at 18:22
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