In Act 1.5.100, Marcellus makes his portentous remark, "Something is rotten in the state of Denmark." Of course, many things are "rotten" in the kingdom: the betrayal and murder of the king by his brother, Gertrude's infidelity and fickleness, and Prince Hamlet's denial of the throne, to name a few.
The theme of decay continues throughout the play. In Act 4.5.204-209, Ophelia compares the beauty and delicacy to the dying spring flowers to her own beloved fathers death:
There's fennel for you, and columbines.
There's rue for you, and here's some for me; we
may call it herb of grace o' Sundays. You(must) wear
your rue with a difference. There's a daisy. I would
give you some violets, but they withered all when
my father died. They say he made a good end.
The herbs Ophelia refers to here are not accidental or random. Fennel is known to be a favorite of snakes. They eat it when they shed their skins. Columbine was also known as a symbol of the Holy Spirit. And rue is probably chosen because of the word play, ie, to "rue" the day.