Thankfully, I've never run into a shiny I never caught. Mostly thanks to cloning masterballs though, a list -
Graveller - explosion; this was a weird shiny, was trying to chain rattata and went into a normal patch and out she pops I was like wth?!
Houndour - roar
Abra - teleport, nuff said
Growlithe - roar
Poochyena - roar
All caught in masters...I never start a game without trading a couple masters to it right away just in case D: I know lots of people get silly about catching shinys in masters, but I almost never trade my shinys that I catch personally; they're my treasures. I did catch a rattata with double edge, but that was with a repeat ball. So far though I`ve never caught a shiny legendary; I`ve been soft resetting since like a week after HGSS came out for a stupid suicune lol at least 200 tries thus far =( SRing hates me. Though thinking about it, I caught a shiny wingull (Yay rotfl) that got deleted when my Emerald crashed and deleted my save data. I've since replaced him, though I suppose that would count. Though I caught him, I lost him. *Shrug* RIP Mokkan ;_; In the original gold I was darn lucky with my shiny koffing; at the time I didn't know wild ones have selfdestruct; found mine in Rocket's hideout. Forget what ball I caught her in, but I didn't have a masterball as I hadn't even finished the game. I was playing the hideout for the first time. And when I caught my random pachirisu I was literally half asleep; I'm lucky I noticed he was shiny and got him. And my shiny patch in my houndour chain was behind a tree; I barely saw it LOL and on my second successful zigzagoon chain two patches were shiny. I have nearly 30 self caught shinys so I have other stories, but those are the most interesting. I frequently catch shinys before the 40 mark on chains, ie my starly at 2 and abra at 4.
I did know a kid that ran into a Galactic grunt with a shiny glameow. And one of my friends found a shiny cherrim in the battle factory in Diamond.