Well...back in the days of Mario 3, I figured out a cheat for it all by myself. I could never beat one of the World 8 levels, so I did a trick with the Warp Whistles and the P-Wing...and I beat the game a few hours later!
Hmm. Over the span of four generations, I've caught four shiny Pokémon (five if you count the plot-standard Red Gyarados)--a gold Magikarp (in Gold, so I never evolved it since I'd just have another reddy), a purple Wurmple, a green Zubat, and a green Machoke.
The last two are on my Pearl game, and at the time I'd logged very little time on it. Compare with Sapphire, where I've played it for over 600 hours and have yet to even *see* a shiny.
And if none of that shiny crap impresses you, there's about a one in 8100 chance of seeing an alternately colored pokémon. Catching it can be hard if you're not prepared for it (it's the same as other pokes of the same type, but you may not be looking to capture anything and thereby have an uber-powerful party or something)