I've been there a number of times when I was stationed in DC. I've been there to just sit on the stairs and watch, to watch a wreath laying by a visiting dignitary (some politition from So. America) and for Memorial/Veterans Day ceremonies. Each time I brought a camera, but never took a picture. For some reason it seemed disrespectful to disturb the somber atmosphere with the sound of a camera clicking away.
I've been there during the guard change; when Taps was played, the bugler located in the distance; and when they had the Army Howitzers firing a salute. All of which was very memorable, but the worst (or best depending on your viewpoint) is when all is quiet, and all you hear is the sound of the horse's hoof-beats far in the distance, knowing that they are on their way to put another hero to rest.