I replaced the cartridge in my Moen shower faucet and now I get water hammering. When I put the old one back in, it stopped.

Your new cartridge is acting a bit faster and shuts the water off instantly, the hammer is caused by the momentum of the water slamming againist the valve and vibrating the pipes. Insure all pipe strapping is very secure and if need be instll a air hammer arrestor under the sink. PlumbingSupply.com - Water Hammer Arresters (Arrestors)