The touch-move rule, or "j'adoube" which means "to adjust", is a rule in chess which states that if a player touched a piece on the board and it was his turn, then that player is obliged to move that piece. This rule was originally intended for more serious competitors. For example, in the Middle Ages the touch-move rule was important since chess was played for stakes. Of course, rules like this cannot always be strictly followed and changes must be made by an administrator of the game - imagine for instance a player who touched a piece and it is illegal to move. Such misconceptions can lead to amusing results.

Here is a good example of the amusing results that may come about from the touch-move rule. A game in which White was likely wanting to play 3.Nc3 but mistakenly moved his queen's bishop on c3. This is an illegal move so eventually, White moved his king (since it being the closest piece to the desired piece) to the only free square: 3.Ke2?? resulting in a sad but amusing checkmate from Black, 3... Qe4#.

Is it a rule that if you touch a piece that can't move you have to move your king? I was not aware of this.

And so, deeper into this rule, what happens if your king is also stuck on it's current square?

Nytik, that is not the case. If you cannot make a legal move with your own piece after you have touched it you can make any legal move.  If you have touched one of your opponent's pieces you have to capture it if you can legally (could be bad if you intended to capture a defended pawn with your own pawn illegally and then had to take it with your Queen).

The old rule I have read was that if you had no legal move with the touched piecve you had to move your king, but ancient as I am it was before my time...

FIDE rules

7.3

If none of the touched pieces has a legal move (or if none of the opponent's pieces which were touched can be captured legally), the player is free to make any legal move.

hmm this is a bit misleading.  If you touch a piece and there is no legal move for that piece, you are free to make any legal move.  If you notice that an illegal move has been made, then you must reinstate the position before the illegal move.  Also, "J'adoube" means I adjust, and is what you say so you can adjust your pieces without being forced to move them.  It is not 'the touch move rule'.