For kids, sports and wildlife photography, it's very difficult to press the shutter at exactly the right time for that "special" image. As smartphone cameras improve, you should consider taking action shots in video mode and then extracting the best stills.
Professionals who spend thousands of dollars on a single lens for cameras that can snap ten frames per second and weigh five pounds have the perfect solution - but I only know six professional photographers. For the rest of us a good quality smartphone, a little time to get the best video possible and an app such as SnapStill to locate and save special images is all it takes. The picture at the right was taken on my iPhone originally as a video.