Mine was actually getting the starter, and finding a favorite pokemon, I thought Cyndiquil was epic cuz I loved fire types, And when it evolved for the first time I pretty much fell in love instantly. And Quilava has been my favorite pokemon since I was 6 :) And then after that was the first time I saw Lance and I was like, "Zomg, Dragons -Shrieks in Terror/Pleasure-"
I was just starting a new pokemon silver for the sixth time with a friend when he told me he noticed a pidgey shining. I looked at it and it was shiny pidgey. DUDE, catch it. Luckily we had pokeballs and were heading back to Elm.
Spending a week straight training my Meganium to level 100 on Mt. Silver. I wasn't exactly the smartest kid and I didn't realize until way after the fact the Elite Four was faster plus gave money which I so desperately needed for Vitamins.
Another time was getting my very first Espeon during the bus ride to school in 4th grade. I hadn't yet known that Eevee would evolve into Espeon and Umbreon since I wasn't big into the internet back then. Named him Sunny and he forever sits on Stadium 2 at level 100 since I fear losing him to a dead internal battery.
When I first turned on the game and started playing. I was with my grandparent in a used clothing store, sitting under the bins, being amazed at the new starter pokemons (I had never seen them before, they were totally new, it was an awesome experience). Every new pokemon I saw was amazing. Silver was also the first pokemon game I actually beat.
Oh I also went to that area with geodudes near the start and fought them to level up all my pokemon up to 10. Took forever but I decided it was safest for some reason (I think they only used defense curl)
On my Gold, when I was probably 11 years old, I encountered my first and only Shiny Pokemon. It was a Flaffy. And I didn't have any Pokeballs.. This experience was so traumatic that I remember it to this day, haha.
Going to the elite four. I could never beat them because I sucked when I was 8, But I had Granbull like level 60 something. With Dynamic Punch that got me all the way to Bruno who would always beat me. This made get a Granbull in Heartgold and try to solo everyone with it. Good Freaking Times..
Uh...bullshit...and you would never need cut so much that you wasted a Master Ball on Rattata...in fact, you would not be able to get through the game to where you have the opportunity to meet Entei without a Pokemon with Cut...
Mine was most likely realizing I had another set of gyms to play. That made me so happy.