I've got a few moments. Not counting all nighters when I first got HeartGold or Black or Black 2, I think my first Pokemon moment would be getting a legitimate copy of Pokemon Crystal for my 6th or 7th birthday (too lazy to do the math). My experience with Pokemon up until that moment had been with fake-carts from Taiwan that contained Pokemon Red, Blue, Green, Yellow, Silver, Gold, TCG, "Super Pikachu Land" (Super Mario Land but with Pokemon!), and some Smurfs game that had Pikachu as the protagonist (Well handheld experience, not gonna list the N64 titles or the anime). I was excited playing this because I finally understood everything that was going on and happening, that I'd actually complete the game for once!
Next Pokemon memory would have to be catching a Shiny Seaking from the Safari Zone in Firered. Was fishing for a Dragonair, ended up hooking that boss. I got excited and scared mostly because it's the Safari Zone, you miss with that first Pokeball and you might not see it again.

Caught it though! Pretty much my first shiny after the Gyarados in Crystal version.
I competed in the 2006 Journey Across America tournaments. Met a bunch of cool people there, trying to make it in. Ended up running into them through and outside of JAA when the Houston Space Center handed out Deoxys. Never actually made it all the via competing though. I got lucky when they hosted a last chance qualifier online, I was one of the first to complete it. Went to Bryant Park, won a few and lost. Played demos of Ranger and Mystery Dungeon, saw Pokemon and the Mystery of Mew early, got a bunch of cool swag, got plenty of event Pokemon (CELEBI!!) and explored NYC for the first time.
tl;dr Pokemon is my life