Shiny Pokemon
Shiny Pokemon are Pokemon that have a different color than those of the same species. Shiny Pokemon are very rare and can be seen in the wild, owned by a Pokemon Trainer, bought in the Game Corner and seen in other places. Many people don't even see one in the whole game. When you meet one, stars will shine around it. If you meet one in Pokemon Colosseum or Pokemon XD, the letters that spell out the Pokemon's name will appear in Gold. Many websites tell you this and tell you that it's based on luck, but I think that it's hard to believe. I will tell you my experiences(Manjyome has too many, so I won't write about his) with shiny Pokemon.
Shiny Pokemon sightings
Pokemon Diamond/Pearl:

Rachel J told me that she saw a shiny Ditto after her PokeRader activated next to Cancalave city. She caught it using a Leafeon, and some Ultra Balls.

Pokemon Ruby/Sapphire/Emerald:
Rachel J told me that she saw a shiny Linoone by Lilycove City and she barricaded it with ultra balls until she caught it.
Alexis E told me that a shiny Magnemite was found in New Mauville in the Pokemon Ruby version.
Pikachu Lover told me of an interesting story about her catching her first shiny in Pokemon Emerald. Here is a quote from the story:
" I was trying to train my Swampert in Route 114 (the Route near Meteor Falls) when I found a shiny Selviper. I almost ran from it, because of the shock of finding my first, but then relised what I was doing and slowly weakened it. After about half of the HP was gone, I started hurling Ultra Balls at the Selviper and caught it at my sixth throw. The Selviper's nickname is Shinyviper."
I saw a shiny Pokemon in my Pokemon Sapphire in the Jagged Pass within 22 hours of play. It was a Spoink and I had a Sableye. Spoink was about level 19 and my Sableye was about level 26. My Sableye wasn't a very strong Pokemon and when it used its Cut attack on usual Spoinks, none of them would faint(most of them would have about 1/2 HP left). I used Cut on this shiny Sableye since I wanted to catch it, but it automatically fainted. Sometimes shiny Pokemon are weaker than usual Pokemon.

Pokemon FireRed/LeafGreen:
My cousin told me that he found a shiny Magikarp while he was fishing, but he didn't catch it because he didn't like it.
Mespirit82597 told me that a shiny Exeggcute appeared in the Safari Zone and it fled.
JL told me about her adventure with several shinies that she saw:
"I've found 2 shiny wild Dunspraces on two island after I beat the elite 4 about 5 times, but I forgot to save and the power on my GBA was very low so I didn't get them. However, one was a male and the other was a female. Plus, I've seen a wild shiny Zubat on floor 2, but when my Pokemon attacked it hit a critical, so I didn't get it either"
From this, remember that if you want to catch shinies, you should always make sure that you take a Pokemon with a move like False Swipe so that you don't KO the Pokemon on purpose and that you should always charge your console and save right after you get them. ^^
Danielle told me that she found a Jumpluff after just 29 hours that was shiny and a Kadabra after 66 hours. She claims that she also has a gold Gyrados and that her Magikarp was blue. However this is not likely since there are only two colors Pokemon can have (besides the gender differences in Diamond and Pearl). Probably, she saw a different Pokemon like Milotic.
There is an issue with most Pokemon games that makes catching shiny Pokemon more complicated. It is the Great Marsh(in Pokemon Diamond and Pearl) or the Safari Zone in other games.
Obviously, you do not use Pokemon to catch Pokemon in those areas. Shinies still occur there! I've heard many people see a shiny in those places and didn't catch the Pokemon. It's obviously frustrating.
Mostly, if the Pokemon is like an Oddish, you'll be able to catch it, but if it's a Venemoth or Chansey, you're likely not to catch it at all.
The best way to insure that you'll always catch the shiny if you see it is to avoid those places and rather trade with other people through GTS to get those Pokemon. You can then breed them to get a shiny.
And if you meet a shiny when it's owned by another person, I guess that you can't catch it then.
In Pokemon FireRed/LeafGreen, you'll see a shiny Espeon in the Battle Tower(or that place where every Pokemon is level 100). If you don't trust me, go there yourself and go with double battles. The first pair you meet will have a shiny Espeon and a normal Jolteon. Everyone gets this, so don't feel disappointed. (Although that Espeon is pretty rare. I wish they would give a shiny Eevee to us after we completed those trainers).

I found my shiny Dratini(named Drakyria) after 5 soft resettings(It is rumored by other trainers that Soft Resetting will increase your chances of a shiny Pokemon. To soft reset, press A+B+Select+Start simultaneously) at the Game Corner in Pokemon LeafGreen at approximately 65 hours of play. Drakyria is an average Pokemon and has average stats.
Pokemon Gold/Silver/Crystal:
I found my shiny Zubat at level 5 after 57 hours of play. My shiny Zubat was found in the forest by the city where the second gym is situated. You can easily find Shiny Gyrados by the lake.
That's all I've caught.
Don't worry if you haven't seen even one, because I haven't seen any in my Pokemon Ruby(after more than 100 hours of play) or my Pokemon FireRed(after 60 hours of play) or my Pokemon Pearl.
Keep trying and you'll get one, because that's how the game is
If you have any sightings, please tell us and if we find your sighting very interesting, we will write about your event.