...I'm sorry, the Original Series had a plot?
Kanto did, for the most part. The story was about a young boy discovering the world of Pokemon, his two travel companions, and we had the whole Giovanni/Mewtwo storyline which was resolved in the movie.
Orange Islands, again, was mostly self-contained and it was so short anyway that it didn't need some huge story, although we did get Charizard's story resolved among other things.
However once you get to Johto, it pretty much just turns into Ash helping whatever filler character needed help with a problem, and going on another badge journey.