I could see how a 4 or 16 ohm
or 8 or 32 ohm
switch could work, but how do switches that just double or half the impedance work?

One is the Kustom MLI monitor speaker.
It has an impedance switch to select 8 or 16 ohms.
http://www.kustom.com/products/pa/switchable_impedance.asp

The other is the Accugroove bass cabinet - it has a switch to select either 4 or 8 ohms. (But I found a thread on talkbass and apparently the switch doesn't measure up to its claims.)

My confusion is how a switch could select just double the impedance. For example: 4-or-8ohms, or 8-or-16 ohms. I can't see how you can series/parallel to get such combinations.

It'd sure be handy if such a switch were possible.

The attenuator is an L-Pad, which has series and parallel resistance elements. The switch probably sets a fixed resistor, which is used as part of a voltage divider. The other part of the divider is a variable resistor. Since speakers are a reactive load, resistance does more than just attenuate, it also acts something as a tone control. But I think that's all way beyond the scope of this discussion. The bottom line is that the switch is just selecting the amount of resistance used in the circuit.

Here's the link to the other switch.
http://news.harmony-central.com/News/2003/AccuSwitch.html
You have to go to the accugroove site to find out more about it.
But as I mentioned - folks who actually measured it say it does't work.