I can list off these kinds of moments right now.
1) Walking through a patch of grass and on the last tile, I encounter a random Pokemon.
2) Encountering a Pokemon 5 times in a row walking only one step in between each encounter (this has happened before)
3) Luck Hax
4) Random Criticals, especially ones that occur at the worst times possible
5) Biking through a cave and a dust cloud containing a Drilbur/Excadrill pops up on the very next tile you step on.
6) Any cave, route, or other that requires a gratuitous amount of HMs
7) The idea of HMs in general. WHY ARE THEY IN THE GAME.
8) Trying to get an egg to show up in the daycare for 5 hours but it never showing up
I could list more, but I don't feel like thinking about it any more at this moment. I'll add more as it comes to mind. What are yours?