True, playing the games have that nolstalgic feeling. Of course, I battle competitively a lot, so that takes more thinking than most children usually do. However, the overall feel of the games makes you feel a bit younger.
Like Cain said, just playing through the story, a little kid on a journey with his pets, really breathes some youth into the hustle-and-bustle life I live nowadays. The battling part also lets off some steam.
Well...not really, actually. I'm old enough now to realize how much the games are lacking (in some areas, not all). The main reason I still play is because I still have a ridiculous amount of fun raising and battling Pokemon. I bought my Diamond nearly ten months ago, and I've played it practically every day (at least some) since. 380 hours is WAY more than I've ever played any game.
That said, playing (and watching some of the old anime) the older games does give me a really nice feeling of nostalgia. So...yeah.
Makes me feel old, if anything. I can completely remember playing Pokémon games on my old-school monochrome Game Boy; no colors, no animated sprites, all of 4 Pokéballs and one region. And now you're telling me that games are in full color with limited 3D graphics, the Pokémon move around when they appear in battle, there are more different types of Pokéballs than I have fingers to count with, there's a good 6-7 regions including Kanto AND the games can go online? The hell you say?
I don't feel like a little kid when i play the newer games (DP and RSE), i feel normal, but when i play the old RBY and GSC games that i remember playing on my black and white gameboy pocket it sure brings back some nostalgic memories and makes me feel a lot younger.