The Slime: It moves around the board making it sticky. Then any piece landing on a slimed square is stuck there forever.
Invent the new worst/most useless chess piece ever!

The Knought. Replaces the Knight, and is only allowed to move to a square further to the rear, but as long as its move is to the rear It is free to make any move it likes.
The dynamic of a game changes quite a bit, as castling is very difficult, and can only be achieved with the help of the opponent.

Certainly conforms with the useless requirement of the Original Poster, but posslibly fails the worst test.

The wall: Moves as king, 2 squares wide, 2 squares tall, starts at d4-d5-e4-e5, can't capture and is uncapturable, and blocks moves.

The skunk: Sits idle in the middle of the board. Whenever it is attacked it releases a horrible odor, making the rest of the game a miserable experience for both players. Cannot be captured.

The Suicide Bomber
You don't know which piece it is and you don't know if it is white or black. It is triggered by a random capture (could be at anytime) and, just like Atomic Chess, obliterating everything in the adjacent squares.

The Admiral Ackbar. This piece sits on a chair hovering above the board and yells "It's a trap!" whenever your opponent is about to blunder. Capturing it is impossible since it is not actually on the board, and if you try to remove it by force your pieces will start to fly up and shoot lasers at you, thus abruptly ending the game (and costing you extra money in medical bills).

The freezer
any peice within a radius of 100 squares from it is frozen, and it can't capture anything
starts on g3 for white and b6 for black
teleports to anywhere on the bord
The "Prince", in honour of Prince Charles of England. This piece would replace the King on both sides, and will just sit there on the home square doing nothing while his mum (the Queen...), and his subjects, do all the work. He quite likes the idea of being checkmated, as being a King looks like a lot of bother. In honour of Queen Elizabeth II, in this set up, the Queen can never be captured, because then the Prince might be promoted to King. And we don't want that to happen...

The tower
so high, nothing can go past it
can't move, too heavy
can't get captured, too big
takes up a(files)*2(ranks) space
replaces pawns
each 1*2 pawn is a tower
causes automatic stalemate
Not a new piece, but a new square defined by a new move, so in the spirit of this thread, I hope.
It's "The Tower of London" square, where a piece gets sent if it forks two bishops, or other members of the aristocracy. This square should be chosen by the forked player, from the empty squares on the chessboard, through a valid move of the forker, to cause maximum torture to him. For instance, "Knight beaten to death by serf for forking Q & R":
The freezer
any peice within a radius of 100 squares from it is frozen, and it can't capture anything
starts on g3 for white and b6 for black
teleports to anywhere on the bord
Within a hundred squares? I like it! Upset the whole tournament....
The burning piece-If you try to capture it all you get is burnt and if u don't move it it will burn through the board and eventually burn through the table. Lucky for you if your on computer. all it does is leave a hole.
"the Post"...it can't move or capture and sits on e4.