You can own them, but you can't do anything with them. From Wikipedia's article on DC gun laws:
Originally Posted by Arroyo_Doble
Possession of firearmsThe car was clearly an assault auto.
In Washington, D.C., all firearms must be registered with the police, by the terms of the Firearms Control Regulations Act of 1975.
The same law also prohibited the possession of handguns, even in private citizens' own homes, unless they were registered before 1976. However, the handgun ban was struck down by the U.S. Supreme Court in the 2008 case District of Columbia v. Heller. The Supreme Court ruled that the Second Amendment acknowledges and guarantees the right of the individual to possess and carry firearms, and therefore D.C.'s ban on handguns was unconstitutional.
Following the Heller decision, the Washington D.C. City Council enacted a set of rules regulating the possession of handguns in citizens' homes. In addition to each firearm being registered with the police, the rules require that D.C. residents undergo a NCIC background check and submit to fingerprinting. The firearms registry photographs the applicant. Residents must take an online gun safety course, and pass a written test on the District's gun laws. Residents must also declare at what address it will be kept. There is a 10 day waiting period from purchase of firearm to possession, and a 30 day period between purchases of successive handguns. Each firearm is registered to an individual only, meaning couples who wish to own firearms must purchase two separate firearms. An individual may not possess ammunition without also possessing a registration certificate in their name. Handgun registrants must be 21. Long gun registration is allowed for persons 18-21 years of age with a NCIC qualified adult co-registering. Handgun models are limited to any handgun appearing on any one of the California, Massachusetts, Maryland or DC Police "approved rosters." Non residents, with a place of business in DC my register a firearm to be maintained at that place of business. 
The District of Columbia does not permit the concealed carrying of firearms. Open carry is also prohibited. A lawsuit was filed on August 6, 2009, to compel the district to issue permits to carry weapons.