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I found loads of shinies over different games. My current file of X holds the record for the most shinies I've found in one game, with 7. Latest shiny find was a Zigzagoon in Alpha Sapphire found via random encounter. Also, there has been two games where I managed to catch a shiny Graveler - Diamond and Soul Silver.
Of the shinies I have my faves are my Duskull from Ruby, because she was the first shiny I ever found so that's why she's special. Then there's the Miltank I found in X, because I love blue shinies although I wasn't a fan of how the shade its blue color looked in 6th Gen (reminds me of how shiny Espeon's green got a bit darker) but still, it's one of my fave 2nd Gen Pokemon and I'm happy I have a shiny one of my own. And my third pick is another of my shinies from X, a Quagsire which I caught on a day that I was suffering a terrible breakdown caused by stress so finding it helped make me feel better.