This was a pretty cool find on YouTube. It looks like this takes place looking northwest on Pennsylvania Ave, maybe around 12th St. You can see the Willard Hotel in the background. The postal worker dumps a few bags of mail onto the streetcar, grabs a few off the streetcar, puts them in his wagon and drives off. This takes place some time in 1903 and the video is courtesy of the Library of Congress.
Here’s another really cool video, this time from 1941. It shows people riding a Capital Traction Company streetcar through the streets of Washington.
Check out the rest of them on YouTube … it’s a great peek into the District’s streetcar past. If I find any really good ones, I’ll post them.