Alright, let's see here...
I am 19, a college student who is just finishing up his first year.
The other day I was talking with a friend of mine who is going to be my roommate next year. Somehow we got on the subject of favorite TV shows as we were children, and I mentioned Pokémon. This of course led into a conversation about Pokémon in general, and when I mentioned that the games were good ways to pass the time, he told me that his mother sometimes plays the games and challenged me to a Pokémon battle next year when we're rooming together.
So, I would say that, yes, Pokémon is aimed more at younger children than it is at adults...but that doesn't mean that it's not something adults can enjoy. There are actually a lot of people my age or older that either still play the games or have fond memories of playing it; I'd bet that if I did a survey of the kids on my college campus, probably about 75% of them would either still play them or have fun reminiscing about them.
I do believe, however, that that phenomenon isn't going to last. Pokémon is still big nowadays, but it's not as dominant as it used to be. When it first came out and the people my age were growing up, Pokémon was the biggest thing around, and none of its competitors were even close. I'd compare its popularity around that age group to the popularity of the Beatles during the British Invasion--there were a few holdouts, but practically everyone was into Pokémon to some degree. Pokémon cards were even banned at my elementary school because they were distracting the students. I could be wrong, but I don't see it as being as much of a force right now as it was when it first came out, and I think that it will probably lose some of its staying power because of it (i.e. there are fewer people getting into it now to begin with, and fewer of them are likely to stick with it).