I have about four moments I can think of right now.
First would be trying to catch a wild Dragonair in Yellow Version (it's possible, just gotta use the Super Rod in the first area, and wait.) Literally took 2 hours just to catch one. Worth it in the end though.
Second, I was battling Lance on SoulSilver with an underleveled team. Of course, his Lv. 50 Dragonite kicked my team's ass. The sad part was that Explocano the Typhlosion only knew Fire moves, and nobody knew an Ice-Type move.
Thankfully when I started a new file, I remmbered to put Blizzard on Golduck.
Third was when I found a shiny on Crystal. Normally this is fine, except it was a wild Metapod. *sobs* WHY ME?!?!
And finally, I was trying to raise an Ekans on Crystal.
Good news: I caught a Tauros.
Bad news: It was around midnight, and I was jamming to a song on my Ipod. Woke my dad up. Long story short, goodbye Tauros+leveled up Ekans.
EDIT: Got another one.
Friend: "Dude, I caught a shiny squirtle using the old rod in Pallet, AND it has Pokerus!!"
Me: "WHAT?! Bullcrap!"
Friend: "It's true! You can catch the starters in certain areas, it's just a small chanc of finding them!"
Me: "F**k you, hacker!!"
Friend's Friend: "He's right you know. Squirtle is in Pallet Town, Bulbasaur in Route 2, and Charmander in Mt. Moon/Rock Tunnel (Don't really remember)."
Me: "Dude, that's impossible!"