I've only seen one shiny, and it wasn't even on my own cartridge. My friend say a shiny Sneasel on her original Gold cartridge, but she was so excited that she pulled her AC adapter out of the wall and her Gameboy had no batteries in it... yeah.
Not once have I seen one on my own cartridges, even though I've put hundreds of hours into each Pokemon generation that exists.
My first shiny was a shiny Zubat in Fire Red (all those Zubut encounters paid off ^.^). The next two shiny pokemon I found were in Pokemon Black and they were an Audino and Zangoose. I have the two event shiny Pokemon also (Haxorus and Red Gyrados)
What about the Black Tower/White Tree Hollow reward dragon?
I've caught / obtained quite a few shinies in my games:
Back in the days of third gen, right before Diamond and Pearl were about to come out, I wanted to get a shiny that I could call my own prior. I really wanted a shiny Roselia, so I searched the route by the daycare forever. Ended up giving the game to my brother because we were stuck at the church for hours with nothing to do because no one was there except us and our dad, and he found a shiny Zigzagoon within a half hour... :P So that was my first (since it was on my game).
My second was a shiny Noctowl I found on my Pearl version when just looking for one of a certain nature (so I was using a Synchronizer). Ended up finding a shiny Calm one with Insomnia. :) Then I ended up encountering a shiny Graveler in Iron Island a few weeks later, though it was unfortunately Gentle natured...
Then comes Platinum, and I was resetting for the Eevee you get from Bebe just to get a certain nature, and I ended up being given a shiny one (I almost reset on it because it didn't immediately register that it was shiny); unfortunately, Lax natured. Then I was synching for a Timid Kadabra on the route west of Veilstone, and I encountered a golden Lickitung, which I then caught. And finally, when I was searching for Feebas with a friend in Mt. Coronet, I ended up finding the Feebas, and when fishing for it (I had brought six different Abra with me to use Synchronize on it), around the tenth one I caught was a shiny. I spazzed so hard on the bus when it happened, haha.
And in my Black version, I encountered a shiny Klink purely by accident when just trying to get through Chargestone Cave (or whatever it's called), but caught it. I think it was Lax... I have a bad habit of getting Lax/Gentle shinies, lol. Worst natures ever... Anyway, then when I was synching for a Krokorok to put on my team, I ended up encountering a shiny male one, with the synched nature and the ability that I wanted :D I was so stoked when I caught it. (I mean, I prefer Krookodile's normal coloring, but I had a f**king shiny on my main Black team. How awesome is that?)
And that's my history of shiny encounters. Not counting events and whatnot, of course.
So anyway, my advice to you if you want shinies, use Synchronizers a lot if it's fourth gen. Fifth gen, idk how the value generation works, but in the fourth, the Synchronizing rolls it over to the next personality value that would give the nature in question, thereby seemingly often triggering a personality value that you would have otherwise missed that makes the Pokémon in question shiny. That seems to be the case with me, at least.
Anticipated games~ Animal Crossing: Jump Out, Luigi's Mansion: Dark Moon, Paper Mario: Sticker Star, Layton vs. Gyakuten, Pikmin 3, Nintendoland