Definitely when I beat the Elite 4 in Pokemon Yellow with my Dodrio and Sandslash. Those are the only 2 Pokemon I used the whole game and I happened to pick ones that had 4x and 2x weaknesses to Ice...lame. But when I beat it I called my buddy on the phone and was so excited haha
I remembered playing Pokemon Gold, and there was this guy who was looking through the window of Professor Elm's Pokemon Lab. He turns out to be your rival, and steals one of the starter Pokemon.
Well here's the funny thing. After bumping into him while he was running away, a policeman came and asked me if I noticed somebody running away. Then he asked me if I could give the person's name. I really wanted to give accurate information to a law enforcer, but I wasn't sure on his name. So I restarted my game, and paid closer attention this time. When I met the guy running away again, he introduced himself as ???. When the policeman asked me for his name, I told him that it was ???. I was very pleased with myself and with how I did my part of being a responsible citizen, and hoped that such accurate information could help justice reign supreme.
It was only years after that I realized that the rival's name wasn't ???. It never occurred to me that the game, at that point, was actually giving me an opportunity to give my rival a worthy name. Unfortunately, it's too late, and I would always know him to be ???.
My most striking memory is when I first beat champion JOHN (don't know why I named him that) in Pokémon Red. My high-level Charizard and Blastoise had both fainted and my only remaining Pokémon was Articuno. Its cry sent me shivers. It wound up winning with just a sliver of its health remaining.
I went back to play Gold after years of it being left on a shelf, and the file was gone. The internal battery that kept the clock accurate had run out, and years of Pokemon were just gone, including a legitimate Mew...
I remember watching this at my aunts house together with my younger brother and sister. We didn't say anything, but from the inside we were dying if Pikachu would really leave. Still brings tears to my eyes, at the age of 22..
In Pokemon Ruby, I turned my Wailord into a beauty queen and entered her in all the beauty contests. Getting the master rank ribbon took many many tries for a very frustrating reason; I never saved my game. I probably won the master beauty competition with her almost ten times, but every time I got the ribbon, I had to go move something, or my battery would die, or i'd get caught up in a lecture and I'd have my GBA immediately powered off, etc. What didn't help was that the other contestants were MAJOR CHEATERS. I was consistantly thrown in second place thanks to some shock technique. Wailord's got all the ribbons now, but still!
I also recall the trip from Johto to Kanto in my old Gold version rather well. I scoured that accursed S.S. Aqua until finally locating the Metal Coat, I was so excited!
PS, Silver in the games is officially Silver. Game freak recognizes him as Silver in every continuity he's included in.
I've been playing since RB, but mine's very recent, BW2 actually:
Let me start off by saying that I believe that BW(and its sequel) is an incredible game. The characters, the music, the starters, the cover legends, the Pokemon, everything in it, I loved.
(I really think that Gamefreak are in a very tough position right now, can they really top BW?!)
In BW2, after the main game, and after all the sidequests and routes, I made my way to the very last area: Nuvema town, the beginning of BW.
Bianca showed up (I love her) and told my new character about her first adventure with my old character. She told him how they held hands and took their very first steps in their grand (and maybe naive) adventure. She then battled me and the BW Rival Theme played. I swear you have no idea how happy that song makes me!
After that difficult battle was over (I was doing a mono-grass run and she took me by complete surprise!), I walked into Nuvema, and its theme started playing. I barely even remember the theme, but when I walked into that town, it sounded like something I've always known
It all just hit me. I was sitting there, in real life, with all my friends around me, they were playing other video games, having dinner, joking around, whatever, and I was just sitting there fully immersed, on the verge of tears and I don't even know why.
I know I wasn't gonna put the game down, finishing the story and visiting all the areas means I can finally start breeding and EV training. But when I reached Nuvema it felt like something has ended and I really did not want to let go.
The only game other than this one that made me feel like I really didn't want to finish it was Wind Waker. (When I realised I was actually minutes away from the final boss I paused and I was considering stopping and leaving the dungeon!). But WW didn't put me on the verge of tears. This sounds very dramatic and silly now that I'm saying (typing?) it out loud, but I don't know.
For me, it was a more recent memory that was important to me, but when I beat Red in HG with my original team of Pokemon, with all of them around Lvl 60, no EV training, and no healing items either. I can't remember how I did it, but I defeated him against all odds
After I finished my Platinum version, I was cleaning my house and managed to find my old copy of Pokemon Red inside its Game Boy. For some reason, it still worked and I loaded my save that was right before the Elite Four. Beating the Elite Four with the team that I had when I was young was extremely emotional. The emotions exploded after the Pokemon Red stopped working a few days after I became the Champion... *sniff*
I bawled when I lost my Pokemon Diamond in the washing machine. Seriously, I cried for an hour straight. It was my first Pokemon game and had my very first Pokemon ever, Infernape (Nicknamed InfernoApe, I was younger and didn't know anything about it, my name was so close though >:3), and it was in my pocket, along with my DS Lite, I had forgotten to remove them ;v;. My team rekt tho, Infernape was a level 95, I remember training it with Starly's bc I thought it was fun to utterly destroy them with Flare Blitz. R.I.P. InfernoApe <333333