I've had too many close calls.
Caught 100% exeggcute, then promptly hatched a 100% Squirtle
All three shiny magikarp I've caught made me tear up a little. #2 was the best because I found him right after the event ended.
Moved into a new apartment a little while back. Wild Snorlax. First encounter, 44%; 15atk. 11xx cp
Edit: even just now as I was thinking about wanting a bubble-strat team. Next three mons I catch have 14-16 cp, favorable IVs, and even type advantage.