I have quite a few.
One: almost lost to a shipper in ruby due to a rather unfortunate string of misses along with a string of shipper getting critical hits. I finally ko'ed it with my him Pokemon.
Two: being beaten by a psychic trainer after above battle.
Three: In crystal I found my first shiny Pokemon
It was a ledyba. Unfortunately I had no idea what a shiny pokemon was. I actually had this moment around the time d/p came out and I discovered the internet.
4: if it counts for unnoficial Pokemon games then one time I was playing Pokemon showdown and had a pretty good winning streak until this guy with a team made entirely of shiny legendary's with maxed stats challenged me without telling me about his team.
5: every single Pokemon ranger game. DO NOT REPLAY THE MANAPHY LEVEL. IT WILL RESET YOUR GAME!!
6: I accidentally killed entei in g/s/c.
7: in hg/as I ran into my second shiny which.as luck would have it was also a shiny ledyba. I ran into it in the same place and this time I actually caught it. About two days later my sister was messing with my game and released it.
8: b/w 2. The water gym leader. I was using a lucario with three fighting moves and a fire move. You can tell how that went.(I won my first time through actually. It just took me a while.)