Normal pawn: moves 2 squares on first move, 1 square after that, diagonal captures en passant
Crazyhouse Style pawn, Whichever side captures it, is forced to place a pawn on, for white 2nd rank, for black 7th rank. If this pawn is captured and there are no squares on the rank available, the side which captured the pawn loses automatically.
Inverted Pawn: Captures 1 square upward (2 if it's the first move of this pawn) and it moves diagonally, but can move diagonally two squares on move 1.
That's all the ideas I have.
The Wanderer: starts on i2 and i7. Moves like a rook but captures like a king.