For me, the first thing I liked about Pokemon was the anime. I loved watching the series, and I loved the idea that pokemon had different types, and each of the types had their own weaknesses and etc.
I remember watching the first.. maybe 3 episodes of Pokemon, and then purchasing the game. It was certainly a more dumbed down version from the show, but in the game, I had an actual choice to make for my Pokemon team.
I always thought after I bought the pokemon games, I would have to play in Ash's perspective and pick his pokemon. Until I realized I could actually do what I wanted.. and THAT is probably what sparked me to keep playing. That and the fact that unlike Ash, I could catch legendaries :D
A lot of speculation goes around that the show is just not what it used to be. I tend to agree to a CERTAIN extent. I still enjoy the hell out of the show, and watch it whenever I can.. but the games themselves offer insane amounts of content, a different story, and a different way to progress.
That's the reason I like Pokemon. :3