according to Serebii.net, the odds of seeing a shiny Pokemon in the wild is a 1/8000 chance. Every Pokemon has a shiny version. They're just really, really rare varieties of all the available Pokemon.
I myself have never ever seen one, and I've been playing the games for sixteen years, but my friend is a few years younger than me has a lot of shinys. I think it just depends on how frequently you play the game.