http://www.chessvariants.com/invention/universal-chess
Withdrawer - To capture, it must move one-or-more squares directly away from the enemy piece.
Advancer - In order to capture, the Advancer must move to a square adjacent to an enemy piece.
Chameleon - To capture, it mimics the powers of its intended victim.
Swapper - may swap position with any piece (of either side) an unobstructed Queen's move away.
http://www.chessvariants.com/other.dir/ultima.html
Coordinator - captures by 'coordinating' with the King. Upon completing its move, the Coordinator may remove an enemy piece with which (1) it shares a file, and (2) its King shares a rank (or vice versa).
http://www.chessvariants.com/difftaking.dir/rebel-chess.html
Recruiter - can change another piece to its own side
The range jumping pieces from Tenjiku shogi: when making a capture they can jump over any number of pieces. But a ranking determines that some of them cannot jump over some others of them.
The emperor from Maka dai dai shogi: it can jump from anywhere on the board to anywhere on the board within some limitations.
The Wuss
http://play.chessvariants.com/wuss
moves like a queen but can not capture and must move when attacked.
I think that the tricky part is in "The attack cannot be blocked". It would mean that having one or any number of pieces in front of your Wuss would not help, the attack from a distance would still count. But one would have to ask this to the inventor.
This is not how I interpret the rules. The "must move" merely means that the other two methods you normaly have to resolve a check (interposing or capturing the checker) are not legal.
Yes, now I got it, thanks!
http://www.chessvariants.com/large.dir/strangechess.html
Stone: Capture a piece by moving to a square where another piece is exactly between your Stone and the Stone's victim.
Halfer: Occupies half of a square.
The Elk
http://play.chessvariants.com/elk-chess
If positioned on a black square it moves like a Rook. If positioned on a white square it moves like a Knight.
One piece I liked was from the game of Waterloo. It has "elite guards". It moves like king or guard except it can jump 2 squares in any direction (see diagram).
But the interesting thing about it was that if it captures a knight it becomes a joker. The joker jumps to all squares within a 5x5 box. It's like capturing the knight lets it jump to the 8 extra squares that it couldn't do before. It basically "eats" the knight and then adds its powers.
The cobra:
http://www.chessvariants.com/large.dir/cobra.html
The chess board becomes bigger when we suddenly start using the points between the squares.