A Method to her Madness

Ophelia: There's rosemary, that's for remembrance.
Pray you, love, remember. And there is pansies,
that's for thoughts.
Laertes: A document in madness: thoughts and remembrance fitted.
Ophelia: 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 violets, but they withered all when
my father died. They say he made a good end.
(4.5.199-209)

    Ophelia seems to have been dealt a poor hand, given Hamlet's hit and run approach to their relationship and his killing of her father. When she finally breaks down, after her father's death, that is, she takes to singing as a form of expression. The songs she sing hold much meaning, as she sings largely of death and loss of innocence. Similarly, the flowers she hands out supposedly to Claudius and Gertrude have deeper meaning as well.
    The first herb she gifts is rosemary. Rosemary, she claims, is for "remembrance." The herb has another important connotation, however. Rosemary is often used to symbolize marriage and fidelity. Obviously, this herb is not going to Claudius or Gertrude. Most likely, it is being handed to Laertes (for remembrance of Polonius) or is intended to convey a message to an absent Hamlet of her love (and his lack thereof).  She then moves on to pansies, "for thoughts." The word pansy was derived from a French word literally meaning "thought" and has been used traditionally for remembrance as well. These pansies are also probably given to Laertes due to her previous choice of rosemary, but because of the more vague connotation, she could be giving them to anyone present.
    After a quick interjection by Laertes, Ophelia moves on to handing out fennel and columbines. Both of these herbs have negative connotations. Fennel is associated with infidelity, but it is also associated with blandishment. With the fennel, she gives concubine: a flower also associated with adultery and deception. Ophelia presumably gifted these to either Claudius of Gertrude, due to their quick and unseemly union. They could, however, also be a representation of Hamlet's faithlessness to her.
    Rue is the next herb Ophelia mentions, and though it is occasionally associated with adultery, it's strongest and most common connotation is that of regret. Rue symbolizes remorse, which is why it is likely handed to Claudius, due to his regret of murdering King Hamlet and taking the throne. It also symbolizes a powerful and lingering sorrow, one that Claudius may never escape for his sins. Ophelia takes some rue for herself as well, but claims Claudius must wear his rue "with a difference." Ophelia is probably wearing rue in regret for the death of her father or of her relationship with Hamlet. This would explain Claudius's difference in wearing the rue, as her motive for gifting it is different. Ophelia also gives a daisy, symbolizing her innocence.
    Lastly, Ophelia mentions violets. Of these, however, she has none to give. She claims they "wilted all" at her father's death. Violets, representing faithfulness, also symbolize love and modesty. These virtues faded, at least in the life of Ophelia, at the death of her father. These flowers all have heavy implications to Ophelia, and they are more than likely meant to convey these messages when looking at the circumstance. There is, to pull on an old saying, a method to her madness.