Wow... Honestly, I can't pick just one moment. SO many great moments have happened while playing Pokemon... So, I guess I'll just list a few off the top of my head.
-Completing FireRed/LeafGreen for the first time. Call me a "Genwunner" if you will, but my fist Pokemon games were RBY, so the climactic confrontation betwen Red and Green, lifelong rivals, at the Indigo Plateau just brings me a rush of energy that no other battle ever can or will. I know exactly how it feels to have a rival who always seems to be just a step ahead of you, and I feel this battle reflects it perfectly. Red has fought his way through eight Gym Leaders and the Elite Four, not to mention single-handedly taking down Team Rocket in the process. And now, just as his goal, the title of Champion, is within reach, who steps right out to take it from him? GARY... er, Green. Anyway, this battle is timeless and legendary, and reliving the famous final clash between my Charizard and Green's Blastoise ALWAYS gets me excited!
-Completing Pokemon Colosseum for the first time. This particular title is the only Pokemon game I've played cooperatively. A good friend of mine visited me the day I received the game as a gift, and we decided to conquer Story Mode. Over the next few weeks, we played every chance we could, and built a good number of memories. Our team: Espeon, Umbreon, Meganium, Entei, Suicune, and Ampharos, grew in strength and overcame impossible odds time and again. Finally, came the final, climactic battle against Nascour (or so we thought). Completing the gauntlet of trainers before Nascour was tough enough! After a long and arduous battle, our team pulled through, and we decided to use the Master Ball to catch Nascour's Metagross. Just when we thought we had won, the true final boss, Evice, stepped out of the shadows to give me one of the biggest surprises in any video game. Realizing our team was fully healed, we engaged in a truly final duel, and managed to win, even snagging Evice's Tyranitar in an Ultra Ball. At long last, we had won, and Orre was safe. Seeing Ho-Oh fly away at the game's ending gave us a true sense of completion, and helped cement a friendship that stands to this day. Many years have passed, and I've still kept and trained the Metagross we captured (as featured in my signature). Sure, it doesn't have perfect stats, but its sentimental value outweighs any competetive statistic, to me, anyway.