A caption attached to a picture helps to let others know the context in which the picture was taken, and also what the photographer was trying to convey, and therefore helps the viewer to better appreciate the picture.
On the other hand, many pictures (such as those found in www.in-public.com) don't need any captions. The picture is so well captured and well composed that it tells the entire story, without any text to support it. I suppose this would be the holy grail.
For instance, my picture of the shoes by the riverside would be completely pointless until I told you I spotted them early in the morning and there was nobody in sight. Then the questions arise.
What do you think? Should pictures be captioned, or left untitled to tell the entire story by themselves?