Technically, Gyarados was my first shiny Pokémon, but that shouldn't really count, as I didn't encounter it by luck—it was part of the main storyline, which forced me to meet up with it. My first shiny was Hoothoot, if I remember correctly. I was able to catch it with only one Poké Ball (without having to weaken it or anything), but it wasn't such a big surprise, though, since its level was quite low. Once I caught it, I kept it on my team and evolved it into Noctowl. When I had beaten the Pokémon League, I eventually decided to have it replaced with a Pidgeot.
My most recent shiny would have to be Litleo, which I've managed to encounter on Route 22 when playing Pokémon Y. I wasn't able to capture it, though. I was trying to weaken the Pokémon a bit, but when I struck it with an attack, it turned out to be a critical hit—making it faint in an instant. ): If I didn't attack it, then I probably would've had it captured by now.