I've caught a few shinies actually.
In a Platinum run through (I think my first one), I found a shiny Meditite and caught it to use on my team, even though I already had a Psychic type and a Fighting type. I was lost on who to fill the slot it filled with anyway. It ended up slaying a bit.
On my Ruby version, I was looking for Jigglypuff, and when I finally found it, it was shiny. Caught it and then caught a normal colored one a few minutes later. Ended up training the normal one to 100.
In Pearl (or Diamond, I forgot), I was going to chain a Snubbul to try to get a shiny, and I found it on a chain of 1, so I was like "Well...that's all I wanted." and left after catching it.
On Blaze Black (which I can't access anymore

), I found a Shiny Croagunk while trying to find Strength
My wall of text...but yah I have pretty decent luck with shinies.