The games are wonderful and addictively fun, no matter what age you're at, whether you're catching pokemon based on how cool they look, or trying to calculate EVs and team balance. And they only keep getting better with every new release (IMO, anyways- I know there's a lot of die-hards who still like to hold on to their original Reds and Blues).
The anime was great for all ages, up about half-way through the Johto arc. I remember my parents liking to watch it just as much as I did back then. It was still tolerable through the rest of Johto and Hoenn. Ever since Battle Frontier, it's been much more fun for elementary-age kids than any other group, and there are some episodes which are barely watchable at all. But for a long time, it appealed to as wide of a demographic as the games- I still go back and watch the older seasons every now and then.