In my country it is legal to take anyone's photo anywhere that person is out in public, no matter their age.
It is NOT legal, on the other hand, to DISPLAY those photos. Which is different from using them for commercial purposes, which is what applies in the States (from what I have heard through TPF).
So if you feel that photographing the happiness and innocence of playing children in a park gives you nice photo opportunities, you are entitled to do so. Though not all the children's parents KNOW that you have the right.
In my country, however, you must not put up those photos for display. If everyone were really, really, REALLY strict about those "Rights to A Person's Own Picture", you'd not even be allowed to share your photos with husband/wife and family. But who can come take a look?
Anyhow, while a photographer may have very good reasons for his wanting to take photos of children or teenagers (beauty, innocence, happiness, interaction, emotions, lovely faces, good light etc), not everyone might understand his/her reasons. Some, whose minds have actually also become kind of "corrupted" by the pervasive fear (fanned by the media, I should say) might easily (too easily) assume that it is, in fact, other things you're looking for when you take photos of children you don't know.
There's the conflict.
If I get clear signals that someone does NOT want me to take photos of their children, I leave it.
Thankfully, I live in Germany, and I only took photos of dancing children doing a ballet performance this spring. No one said anything against it. Phew!