Check out this map from the National Capital Trolley Museum's website:
Clicking on the map will let you see the routes that were in use in 1958, just a couple years before the end of streetcar service in DC. Many of these rail lines still exist—they were simply paved over when the streetcars were taken out of service. You can, of course, still see some of the old tracks in places like Georgetown:
Photo by Kmf164
Dan Silverman of Prince of Petworth has a photo of some old streetcar rails being torn up as part of the Columbia Heights streetscape project, and I saw some old rails being disposed of during the reconstruction of 11th Street NW between Massachusetts and Rhode Island Avenues.
Some of the old rails are making themselves visible without construction projects. Check out these photos from the corner of Florida Avenue and 8th Street NE. This is right in front of the main gate for Gallaudet University.
The curved pavement cracks in the first and fourth photos show where tracks that are hidden just beneath the surface are making their presence known. Interestingly enough, this corner is part of the proposed second phase of DC's new streetcar network. Looks like these tracks aren't willing to be replaced without a fight!