NACHOE!, I think you hit the nail on the head. Great explanation.
Well, if it wasn't for the cute monsters one could train to grow, it had to be the gameplay, the incorporating of strategies, trading with numerous people, the challenge to catch them all, the storyline, anything really. RPGs are popular in Japan, but they rarely do well in America (if not overseas in general). Pokémon made a name here because the anime got popular. If I'm not mistaken, the vast majority of people who play the games did it because of the anime, and everyone knew what Pokémon was. Why not hop on the bandwagon?
What I enjoy about Pokémon is how wide-spread they are. There's something for everyone about the franchise. For me, it's the games and the story in the games (mainly Mystery Dungeon, probably my favorite game of all the Pokémon games) or sometimes the anime (though the movies have better stories than the series itself). Even though it's marketed at children, which shows in its cuteness, there are rather mature things like complex morals the games have been having lately, or EV training. There's always something that keeps us coming back to it.
Pokémon's popularity may wane over time, but they'll always come up with new ideas to captivate people again, and the audience will grow even more. You know, Mario's rivalry with Sonic is rather inaccurate, don't you think? If anything, Mario should find a rivalry with Pikachu, since the two are way up there in the best-selling franchise games of all-time. Especially since both had a hand in helping video games and Nintendo stay in business. Mario was released when the NES was starting to falter, and Pokémon saved the GameBoy and Game Freak.
But I digress. Pokémon is going to live on for a long time, I can't see it going anyway anytime soon.