My first Pokémon memory wasn't of the Games, but the Anime. Living in Australia back then, the only outlet for Dubbed Anime was a small 2-3 Hour morning TV block called Cheez TV. While the Anime they did get was some of the best at the time back then (like the only known official Dub of Tekkaman Blade, renamed to Teknoman), the most relevant was the airing of Pokémon.
I got up one school morning to get organised, and was switching through the channels before freezing on the channel with a Cartoon I had never seen before. I had just happened to come in just as one of the key points of Ash's career was happening - catching his very First Pokémon, Caterpie!
I kept watching the episode, hoping that it'd tell me the name of the show at some point, but the producers of Cheez TV had cut all the non-episode parts for time. I would find out the next morning though, as the Title Sequence was left in - soon after, advertisements for the Games started airing, and I got a copy of Pokémon Blue Version when it came out...
Yes, we actually got the Anime before the games down here. Though if I wasn't hooked on the Anime back then, I would probably never have even noticed the Pokémon games until much later...