Ah, the games GSC... in my opinion the greatest Gen ever...
But aside from that, my favorite memory from GSC was finding out you could go to Kanto. Seriously, I remember going to Olivine before beating the E4 and getting turned away. After I beat the E4, I never realized they wouldn't turn me away again. So I just kept beating the E4 over, and over, and OVER! Until my Typhlosion was level 100. Then beat it about 10 more times. Finally, I got the courage to stand up to "the evil man at the port" and talked to him. I was like "Really!? I can actually go to KANTO!?" I threw down my GBA and danced around the room (I was young). Finally, I picked it back up and appeared in Vermillion. And with my lvl100 Typhlosion, I swept through all of the Gyms. Beat the E4 even more because I didn't know Mt. Silver existed. Then one day, as I walked up to Victory Road, I noticed (for the first time) that there was a passage to my left. So I walked down it. Found a cave, went through it, can to a wide open space with only one path to go to, saw some dude, talked to him, and a battle began. 1HKO'ed every pokemon Red had with my Ty's Flamethrower.
And that's when I realized I had trained him waaaaay too much. Then I saw a Larvitar. And never loved another game as much as I did that day.