Let's see...My first legendary Pokemon was Zapdos, on Pokemon Red. I received a copy of Red for Christmas back in '98, and the next day I found out my friend had gotten the same game (his brother got blue).
I was going through the Power Plant sometime in early '99, and happened to see a bird by the exit. Curious, I went to talk to it, it cried and a battle started. The next thing I knew, I was looking at a Zapdos around the same level as my party. I did fail on my first try, and ended up smacking it one too many times...it croaked. Luckily I saved before entering the place, and got it on my second try.
I was rather excited, as I had never seen a Zapdos before, and the next day I went to my friend's house. I pulled out my Gameboy (that's right, I still owned an original Gameboy at that point) and smugly pointed to my newest Pokemon. He laughed, retrieving his own Gameboy Pocket. My friend not only had Zapdos, but Articuno as well. Hahaha....