Hummm... waaaaay back, in a Ruby game that's long gone, I found a phanpy in the Safari Zone. It eventually became a donphan.
I'm sure that I found a shiny tentacool once.
But in the more recent stuff...
Electrike in my Normal Monotype Challenge [Em], now in my box.
Saw a shiny poochyena once, in a gen III game. Before I had pokeballs.
A shiny starly in my Diamond game... again, before I had pokeballs (although if I had attacked it to try and weaken it it would have died instantly <`_<; )
My Pearl game gave my a geodude (boxed)
Platinum eventually gave me a budew [box]
My White has given me a ... tadpole. Word. Otamaja thing... um... NAME, BAH. I keep calling him Timcampy by accident [HM]. Also saw a tangela... and forgot that I had my Fly Master with me, so I burned it with Will-o-wisp and it ended up fainting (any actual attack probably would have fainted it.) I was at a serious dilemma about 'SHOULD I USE MY MASTERBALL?!'
My Emerald Nuzlocke gave me a shiny lotad, now lombre.
My Crystal Route 1 Challenge, which gave me a shiny raticate and ponyta (why do I get the pretty blue shinies in the games in which I can't use them?) [box][box]
And then there are my ridiculous games: Diamond Nuzlocke and Heart Gold.
In my DNZ, in less than three days, I found two wurmple and a bidoof- now two dustox and bibarel (notably, this was in the same week that I found both my R1Ch shinies.)
In HG... a sentret and a ratatta before I could catch them (also, any attack would be OHKO, given that my totodile was, respectively, level 29 and 38), a pidgey- now a purdy pidgeot- and a pinsir, from the Bug-Catching contest. We won that one, by the by. [Team][HM]
(More recently in my actual games I have started taking photos of the shinies when they appear (which is how I know my totodile's levels from HG.) It's a... nice... memento, I suppose)