| Ronald Reagan Washington National Airport, code DCA, is the closest airport to the center of Washington, D.C. It is located due south of the city on the other side of the Potomac River, in Arlington, Virginia. Once known simply as National Airport, it was christened with its current name in 1998 by—brace for irony!—President Bill Clinton.
National has served the District's air travelers since 1941, when it was dedicated by Franklin D. Roosevelt. It replaced Hoover Field, Washington's first airport, which was located just west of where the Pentagon sits today, and noted for the fact that a city street crossed its runway, necessitating a level crossing-like gate arrangement to stop traffic so that planes could take off.
The reason the airport is named for Reagan—at least, this is why I think it's named for Reagan—is that before 1987, it was operated directly by Congress as though it were a part of the District. Reagan changed control of National to an independent airport authority run cooperatively by the District of Columbia and the State of Virginia, which officially took it out of the hands of the feds. In theory. Capitol Hill still has a lot of say in how the airport is run.
Along with LaGuardia Airport in New York City, National was one of the first "modern" airports in the United States. Also like LaGuardia, it has shown its age. Widebody aircraft cannot land at National, because its main north/south runway, 1/19, is far too short to accommodate them: only 6,800 feet long. Larger planes can only serve the nation's capital through Dulles or BWI.
This runway also plays host to one of the wildest approaches on the planet, known as the River Visual. DCA is located due south of the National Mall, and The Mall happens to be restricted airspace up to 18,000 feet. So, to avoid the real possibility of being shot down by military SAM's, pilots aren't allowed to fly straight in on a southbound approach to Runway 19: instead, they have to manually fly the plane down the Potomac and line it up with the runway at the last minute. USA Today employees in their skycraper at Rosslyn used to say that they could see passengers inside the windows of airplanes flying by. littlerubberfeet has informed me that National doesn't have a TRACON facility, because of its need for direct control over departing and arriving aircraft.
This approach was discontinued after September 11, 2001, when the whole airport was shut down: obviously, nobody liked the idea of airplanes flying that close to the White House and Pentagon. National did not reopen until October 4, and was not operating at full capacity until March of 2002, when the River Visual returned. Congress also passed a law limiting aircraft at National to no more than 156 seats, making Boeing 757's and other mid-size jets illegal at DCA. (It's also illegal now to leave your seat within 30 minutes of taking off or landing at DCA: thanks to lunchstealer and Servo5678 for that tidbit.)
By federal law, National can only offer direct flights to destinations within 1,250 miles of the capital: in 1999, the government authorized service to four cities outside this radius (Denver, Phoenix, Las Vegas, and Seattle). Longer-range flights have to use Dulles or BWI.
Still, National currently has flights to 69 cities in the US and two cities in Canada, and accounts for some 13 million passengers per year (prewar figures). Even before 9/11, National was experiencing a major traffic downturn: during the 1990's, traffic averaged 15-16 million passengers annually.
Sources: http://www.mwaa.com/national/ and http://www.audishopper.com/terps/p56.htm | 
