Three. moments for me. First, I placed a Level 30 Cacturne with a few perfect IVs in the GTS. One week later, Level 100 Italian Mewtwo. *shrug* I placed the Mewtwo in my game in the GTS and got a Yveltal, so I finished the trio. Speaking of which, a few months ago, I was attempting to catch Zygarde. 20 Ultra Balls wasn't enough. I was using all my junk balls, like the odd premier ball. Only ball left, one Pokè Ball. I through it, and with it my fear and hope, and I caught it. I freaking exploded with happiness. Third lucky moment was when I hatched a shiny Gible after only 18 eggs. Once again, explosions of joy. I've been pretty lucky so far, and I'm hoping my luck continues.
EDIT: Just checked the IVs of the Italian Mewtwo, they are: 31/x/31/x/x/31 So not bad.