The best solution to this that I've found is the Safety 1st Finger Pinch Guard (click here to check price on Amazon) which is basically a U-shaped foam blocker that you put on the side of the door.
In comparison to previous product family, there is a pinchguard that not only prevents the little fingers from jamming, slumming when a kid shuts the door hard, but also can be put high enough that a kid can't reach it.