Be an Observer
Whenever I'm trying to take photos of my kids in action, they act differently. They know the camera's on them and I either get a goofy face or the back of their head and a plea for "no more pictures"!
If you have a camera with interchangeable lenses and a zoom lens you might want to try to get out of the action for bit. You might notice a change in your subjects if they forget you're "there" with them. I can be across the room and still get some great shots of the family interacting all because they don't realize I'm still taking photos of them.
I was 3 rooms away when I took these pictures of the kids playing some crazed Ninja Turtle game. I'm sure some day I'll look back at the chaos fondly...
Having a camera with a zoom lens also lets you get close to the wildlife that may be traveling through your front yard. :) I'm not wanting to get too close to something with horns this large (and sharp!) so I used my zoom lens to keep safe!