OK camera gurus, this may have been discussed before. But I don't hang around the Trail Cameras forum much and the search feature didn't turn up anything.

I'm thinking I could wire a regular 12 volt car battery to my old Moultrie M-40 camera. Would that work, or destroy the camera circuitry?

12 volts is 12 volts if that's the voltage your camera runs on.

How many batteries of what type do you insert in your camera?

Semisane: I did a search for Moultrie M-40 Gamespy TrailCamera specification.
Check out: http://www.huntland.com They give a good comparison chart for I-60, I-40, M-40 and D-40. These cameras all use 6 "D" cell batteries and have a 12 volt external port. The M-40 is the only one that will not take night video. All these cameras are limited to 4GB SD cards.
Check out the post "Cheap Camera using lots of batteries" by Shoulder Strap. I (littlearrow) replied to his post explaining how I hooked up a 12 volt battery using the external 12 volt port. Your camera should have a resistor to cut back on the 12 volt power for this purpose. Caution: 1)make sure the camera is shut off when installing or removing batteries, 2)the center of the barrel plug is positive and the wire with the white tracer or dotted tracer is positive. Do not reverse the wires when connecting to the battery or you will fry the 12 volt external system. I used this system on all my Wild View Ez Cam and Spy Point IRB trail cameras. For a trial, just borrow a battery from your ride on lawnmower, golf cart or skidoo if you have one. Charge up the battery and do a check with a multimeter when checking your camera. Don't let your battery go below 5 to 6 volt before recharging. Hope this helps.