I was once playing the Sapphire version, and I ran into a shiny Poochyena. Normally, that would've been a good thing, but in this case, the timing couldn't have been worse. Guess when and where I ran into it?
On Route 103, on my way to battling Brendan for the first time. A point in the game where it's impossible to catch Pokemon, because you haven't yet obtained your first Poke Balls.
I was also a victim of the dreaded "Safari Zone Pokemon flees" episode. This time it was a Xatu, in the Emerald version.