For years, nonprofits have used the .org extension on their websites to distinguish themselves from for-profit corporations, which typically use a .com extension. However, the registry for websites has never regulated .org in a way that prevents anyone from using a .org domain name, whether they are a nonprofit or not.
A new plan to create numerous new extensions for specialized businesses could introduce a new nonprofit extension as well. One proposal would create an extension of .ngo and only nonprofits would be allowed to register a domain with the .ngo extension. Read the recent Chronicle of Philanthropy article which describes the possible changes.