This article aims at beginners only. When we talk about hanging pieces or pawns, the general understanding is that a piece without support is called a hanging piece. I would like to propose a different categorization, and one which can significantly reduce the number of blunders by just observing and understanding them.
I largely divide hanging pieces into two categories:
A) Pieces that have no support or can have their support removed:
Pieces that have no support, or can have their support removed, are technically undefended. With pieces that are supported like this the attacker always just remove the support and then they are just like undefended pieces.
This is a variation from the game Miguel Najdorf vs Robert James Fischer, 1966 (White to move)
This is very simple, Qc8 check wins the rook on b7.
Miguel Najdorf vs Robert James Fischer, 1966 (White to move)
This is the same scenario as White can first play Nxd6. In the game Fischer resigned in view of Qxd6 and now Nxb7 and we achieved position A in case of Rxb7. Of course Black can’t trap the knight with Qb6 or c7 because of pawn to d6.
B) Pieces performing crucial tasks are always hanging:
Here the piece is performing or going to perform a crucial defending role. It is therefore always hanging no matter how many times it is defended. The game is usually over once it has been captured.
Here’s a position I composed myself:
Here the bishop on c5 is defended three times but this bishop is going to perform the very important task of preventing checkmate vai Qh6. So this bishop is hanging no matter how many times it is defended. White can win the game with Rxc5.