I guess one of mine was when I was walking around, in the area just after you leave Fortree, trying to train my Dodrio and Absol. First encounter, Shiny Marill! Dry internal battery, Pokemon Ruby, and I met a shiny. I panicked, so I used up my masterball. It clicked, and I saved a million times. My first legit shiny...I was so happy.
My second would be the seventh gym. I was horribly underleveled and the SOlrock and teh Lunatone kept killing me. Usually, I would get them to the reds, then they'd heal up with a Full Restore or something. I got so angry, and I was down to only Swampert and Gardeivoir...and both were about to die. So I desperately used Dive with Swampert, hoping they couldn't hit me. THey did, and I was at like 1 HP, the other used a stat boost. Swampert was underwater. Next turn, that Dive One-hit KO's one of the pokemon! I was like 'What the---' then the one remaining is attacking Gardevoir. Dive again with Mudkip. Gardevoir gets to really low HP...and the dive one hit KO's that remaining pokemon. I was so confused. It wasn't even critical. And every other tiem I used Dive, it only put them down a really small amount.
A third would be the Groundoun Battle. I had SR'ed(soft resetted) so many times, because either A. it killed all my pokemon or B. I killed it. I was underlevelled. Plus, my masterball was gone, as I used it on Shiny marill(Shiny Azumarill now.) I was panicking. And playing on my DS Lite. So I threw the Ultra Ball and closed the DS Lite. See, I try strange methods...including closing, and then opening to see if it was caught. My volume was at full, and I heard three jiggles. I didn't hear it break out, so I opened my DS, feeling triumphant...when it gave me a horrible look. It wasn't caught. I was like 'What the--' and wondered what just happened. SO I threw another ultra ball, closed my DS Lite and listened closely....Jiggle...Jiggle...Jiggle...DING! It was caught! I opened my DS, laughing like crazy. I did not expect that...at all.