In Washington, DC nothing is allowed to be built higher than what?

Buildings may not be higher than 130 feet, or the width of the right-of-way of the street or avenue on which building fronts. This has been law since 1910.

The original act restricted the heights of any type of building in the United States capital city of Washington, D.C., to be no higher than 110 feet. In 1910, the 61st United States Congress enacted a new height restriction law limiting building heights to 130 feet, or the width of the right-of-way of the street or avenue on which a building fronts, whichever is shorter.

https://en.wikipedia.org/wiki/Height_of_Buildings_Act_of_1910

There is an urban legend that the height limitation is based on the height of the Capitol and/or Washington Monument. This article explains that this is not the case, and that the height restriction has more to do with the founding father's ideals for how the capital city should look.

One of the most widespread myths I hear from out-of-towners and Washingtonians alike is that the height limit in DC states that no building can be taller than the dome of the Capitol, and that the limit was enacted to preserve views of the Capitol and Washington Monument. This is just plain wrong, and I'm here to tell you why.

http://www.welovedc.com/2009/05/19/dc-mythbusting-the-height-limit/


Further discussion of the myth:

It's a popular myth that the Washington Monument is decreed by law to be the tallest building in the District of Columbia. However, D.C. does have height restrictions that leave the 555-foot-tall monument and the Capitol pretty much unchallenged -- and create a pleasant atmosphere few other major cities can achieve, planners and architects say.

"President George Washington issued the first building height regulations for the city in 1791, concerned as much about structural and fire safety as about urban design," wrote architect Roger K. Lewis for The Washington Post in 1994.

http://www.bizjournals.com/washington/stories/2004/02/16/focus5.html