Smart Chess-board (possibly using RFIDs?)
As I read your post an idea came to me that must be obvious in its simplicity.  Since a chess board has pieces already on it we can simply use hall-effect sensors (dirt cheap) under each square and each piece has a magnet at its base.  Since pieces on a chess board move from one square to another and the initial position of all pieces is known/constant, the detection of a move would be that a piece is lifted from the board (hall effect sensor detects a magnetic field removal) and a piece being placed on a square would be detected by a hall effect senor addition of a magnetic field.  We wouldn't know which piece is placed on a square but we can calculate it by remembering what piece was lifted and it can only be the piece that was placed.