Do people ever do anything with effigies other than burn them?

It is also often used when referring to religious iconography. Another common usage (about as pleasant as the fire one) is the practice of hanging someone in effigy, which involves leaving a hanging image (usually crudely rendered) of the person as a protest.

Yes, they stick pins in them. When, in a previous life, I was a witch, I made wax effigies of people I wanted to die and stuck pins through the heart. If I was merely a little pissed off with them I would just stick a pin in an arm or some place similar.

Isn’t a scarcrow a type of effigy?

They’re also hanged. If you want to get more creative, you can:

Tie it behind the car and drag it,
Lock it in an outhouse and tip it over,
Go to a junkyard at 3:00 AM, piss off the dogs, and toss it over the fence,
Set it in front of a TV set and make it watch reruns of Green Acres.

I remember when I asked my friend, Peter Scandori, what the word effigy meant, and he said, quoting him exactly, “Those are the letters after E, in the Italian alphabet.”

His sense of humor is definitely “different,” to be sure.

People do a lot with effigies, e.g. The Wax Museum. Another name for ‘effigy’ is ‘idol’.
The fact that idolatry is so explicitly prohibited tells you that it has been done… A LOT.

What about those blow-up dolls they sell in the back of the sleazier men’s magazines?

They should be blown up, definitely. They don’t feel at all like the real thing, but I’ve had some better discussions with some of them, than I have had at family reunions I’ve attended.