For a time, Denmark was an elective monarchy, meaning that the king was chosen by council rather than heredity. Hamlet was away at school when his father died, and in one line he says:

He that hath killed my king and whored my mother,

Popped in between th' election and my hopes,

Thrown out his angle for my proper life

I hate using wikipedia as a source, but I don't have access to anything else at the moment. According to the article on the list of Danish monarchs:

The kingdom had been elective (although the eldest son or brother of the previous king was usually elected) until 1660, when it became hereditary and absolutist.