At over 555 feet the Washington Monument was once the tallest building in the world, and is currently the tallest building in Washington D.C,
Technically, there is no law that requires that all buildings in Washington D.C. stay below the height of the Washington Monument. However, the Height of Buildings Act of 1910 restricts all buildings in Washington D.C. to being no higher than the width of the adjacent street plus 20 feet. Thus, a building on a street that is 130 feet wide could only be 150 feet tall. To be taller than the Washington Monument without violating this law, a building would need to be on a street that is over 535 feet wide.
There are a few buildings that are exempt from this law (Basilica of the National Shrine of the Immaculate Conception and the Old Post Office Building to name just two) however, none of these buildings are as tall as the Washington Monument.