I have a 2002 Dodge Neon with around 86,0000 miles on it. It seems when ever it is damp out and I need to break there is a strange knocking sound. It sounds like someone is laying under the car and bouncing a ping pong ball against the under carriage. It comes from the rear, although it is hard to figure out if it is on the driver side or passenger side. If I had to commit to side, I would say passenger.
I would take it to a indepedent shop and have your rearend suspension checked and if that is ok have them pull your brake drums to see if they are ok. You need to have this checked because it could be a safety issue!