The scaling problem was because bone's IK Target was itself. (D'oh!) That caused it to implode.
I guess the only way it can point more at itself is to shrink into oblivion.
The IK Target should be an unrelated bone. Usually one having its root located at the tip of the bone with the IK Constraint. By "unrelated" I mean it should not be a parent or a child of the IK-constrained bone.
From what I have observed, it shouldn't be related to any of the bones in the chain, actually. I believe this means that if you want the target bone to follow along with the armature properly you need to have a bone it copies its location from, using a Bone Constraint. Remember it like this: "No targeting your own family".
Also, there are two types of targets in IK: An IK Target, and an IK Pole Target. The terminology had me mixed up. The IK Target is the bone the tip of the IK-constrained bone will point at, and the IK Pole Target is the bone that the chain will bend toward (like a knee).
When adding an IK Constraint, first select the bone that will be the IK Target, and then Shift-select the bone that will be constrained. Press ShiftI and add it to the Active Bone.
Here's a simple example setup:
- Remember to do Parenting/Unparenting in Edit Mode, and Bone Constraints in Pose Mode.
- Leave some bend in the knees in the direction of the IK Pole Target
- You may also have to rotate the Pole Angle in the settings of the IK Constraint. (I don't know why this is sometimes necessary and sometimes not.)
I think I've just overcome one of my biggest hurdles in rigging. Everyone, feel free to correct me or add something if my understanding is incomplete.
This video helped me to get it.