Answering machines require energy 24 hours a day, 7 days a week.  According to 50waystohelp.com, the annual energy savings if all answering machines in US homes were replaced by voice mail services would total nearly two billion kilowatt hours.

Not to mention, it is one more plastic, electronic device that will likely end up in a landfill.  If you do rid of it, please take to an e-waste collection center.