Where did the expression " there is something rotton in Denmark " come from?

Shakespeare- Hamlet, if I remember right. It's a line in the play. Like many English expressions, it got its start from good ol' Billy Shakespeare.

The story is "Hamlet." Act I, Scene 4: Marcellus (an officer) says "Something is rotten in the state of Denmark," having just seen the ghost of Hamlet's father, the late king of Denmark.

The phrase means "things are unsatisfactory; there is something wrong."
It is often (mis)quoted "There is something rotten in (the state of) Denmark."

"The good Dr. Gerard did not explain?" Sarah said, frowning:
"I don't understand Dr. Gerard. He seems to think --"
"That there is something rotten in the state of Denmark," quoted Poirot. (Agatha Christie, _Appointment with Death_, 1938)

"Even the Republicans are embarassed and feel endangered by this deal and they want to save themselves," she said. "There's something rotten in Denmark, and they want to make sure the smell doesn't attach to them." (_Newsday_, August 30, 1994)

http://www.phrases.org.uk/bulletin_board/12/messages/1184.html

A variation - Something is rotten in the state of Denmark

http://www.phrases.org.uk/meanings/327500.html

What it means is that Hamlet suspected his father was murdered. Which he was, but at that stage he didnt know this.

This is one time when the popular misquotation—"Something's rotten in Denmark"—is a real improvement on the original. But you ought to be careful around purists, who will also remember that the minor character Marcellus, and not Hamlet, is the one who coins the phrase. There's a reason he says "state of Denmark" rather than just Denmark: the fish is rotting from the head down—all is not well at the top of the political hierarchy.

There have been some hair-raising goings-on outside the castle at Elsinore. As the terrified Horatio and Marcellus look on, the ghost of the recently deceased king appears to Prince Hamlet. The spirit beckons Hamlet offstage, and the frenzied prince follows after, ordering the witnesses to stay put. They quickly decide to tag along anyway—it's not "fit" to obey someone who is in such a desperate state. In this confused exchange, Marcellus's famous non sequitur sustains the foreboding mood of the disjointed and mysterious action. And it reinforces the point and tone of some of Hamlet's earlier remarks—for example, that Denmark is "an unweeded garden" of "things rank and gross in nature" (Act 1, scene 2). When his father's ghost tells him his chilling tale in scene 5, the prince will realize just how rotten things really are in Denmark.