Short answer
No. One king cannot capture the other king, and in fact the two kings can never stand on adjacent squares. No piece in chess ever captures a king at all; instead, the game ends when a king is checkmated.
Why kings cannot be adjacent
A king attacks all the squares next to it. A king may not move onto a square attacked by an enemy piece, and an enemy king counts as an attacker of those squares. So if one king moved next to the other, it would be moving into check, which is illegal. This is why the kings always keep at least one square between them.
This follows from the general rule covered in how the king moves: a king can never end a move in check.
Why no piece captures a king
Chess does not allow a capture of the king. When a king is attacked, it is in check, and its player must respond immediately by moving the king, blocking the attack or capturing the attacker. If none of these is possible, the position is checkmate, and the game is over before any capture could happen. So there is no scenario in a legal game where a king is taken off the board.
Can the king capture other pieces?
Yes. A king can capture any enemy piece on an adjacent square, including a queen, rook, bishop, knight or pawn, with one condition: the piece must not be protected. If another enemy piece defends it, the king would land on an attacked square, so the capture is illegal.
This is the answer to the question of why a king “cannot eat” a queen or rook in some positions: it can, unless that piece is defended. It can capture a bishop under the same condition.
Kings and the opposition
Because kings cannot touch, they sometimes face each other with one square between them, and the player who must move may be forced to step aside. This is called the opposition, and it matters in king-and-pawn endgames, where the king becomes an active piece (see the chess strategy guide). The idea is to use the rule that kings cannot be adjacent to win or hold ground.
FAQ
Can kings touch in chess? No.
Can kings attack each other? Kings control adjacent squares, which restricts where the enemy king can go, but they cannot capture each other.
Can a king capture a queen? Yes, if she is unprotected. For the other side, see how to capture a queen.
For a complete summary of piece rules, see chess pieces: names and how each moves.