In act 1, scene 5, Hamlet uses this metaphor after talking with his father's ghost:

Yea, from the table of my memory
I’ll wipe away all trivial fond records (1.5.104–105)

He is specifically referring to his mother here, wishing to wipe away all evidence of any "fond" time from his childhood with her, as she has so dishonored his father. There is also a connotation in this metaphor of a mother's duties to provide for her children, alluded to with the image of a table. Hamlet is showing that his mother has failed in her responsibilities.

In another conversation with his mother, Hamlet compares his father to his uncle:

Have you eyes?
Could you on this fair mountain leave to feed
And batten on this moor? Ha, have you eyes? (3.4.73–75)

Here, Hamlet uses a metaphor to compare his father to a "fair mountain," full of beauty and opportunity with a view of the future. By comparison, his uncle is merely a "moor," empty and void of hope. He laughs at the sharp contrast of their characters and at his mother's seeming blindness to the choice she has made.

Laertes cautions his sister about Hamlet's affections:

For Hamlet and the trifling of his favor,
Hold it a fashion and a toy in blood,
A violet in the youth of primy nature (1.3.6–8)

He is using a metaphor to warn Ophelia that like a violet, the beauty of Hamlet's affections will be short-lived, and that she shouldn't put too much emotional investment into his advances.

In act 2, scene 2, Rosencrantz uses personification with a dose of irony:

None, my lord, but that the world’s grown honest.

Claudius has fetched Rosencrantz and Gildenstern to serve as spies on Hamlet, and when Hamlet asks the pair of old friends what new things are happening, this is what Rosencrantz tells him. The personification highlights that Rosencrantz himself is being anything but honest with Hamlet, and the world hasn't grown honest at all.

Claudius himself uses personification to describe Ophelia's troubles later in the play:

When sorrows come, they come not single spies
But in battalions. (4.5.87–88)

In these lines, Claudius is describing to Gertrude how much Ophelia has suffered. Her troubles have not come individually, but have attacked her all at once. He blames this "batallion" of pain for Ophelia's seeming break with sanity.

Personification and metaphors are woven throughout Hamlet to provide continually deeper and complex meanings for the characters and plot.

In act 1, scene 2, when Hamlet rebukes his mother, Gertrude, regarding her description of his behavior, he uses a metaphor in which he compares his tears over the death of his father to a river.  He calls it "the fruitful river in the eye" (1.2.83).  The river is fruitful, presumably, because Hamlet has cried a lot over the loss of his father. Comparing those tears to a river draws attention to how many he feels he has shed.  He is arguing that he does not "seem" grief-stricken but that he truly is so.

In his famous "To be or not to be" speech in act 3, scene 1, Hamlet uses several metaphors.  First, he asks,

Whether 'tis nobler in the mind to suffer
The slings and arrows of outrageous fortune,
Or to take arms against a sea of troubles, 
And, by opposing, end them? (3.1.58-61).

Here, he compares bad luck to "slings and arrows" to show how much of a negative effect luck seems to have on some people's lives.  He further compares the multitude of troubles that plague us during life to a "sea," emphasizing how numerous and great they seem to be.  He uses another metaphor to compare death to sleep (lines 61-62), moving on to compare whatever it is that awaits us in the afterlife to a dream (lines 66-69). It is the impossibility of knowing what these dreams will be like—good or bad—that makes us hesitate when we begin to consider death as a relief from "outrageous fortune" and our "sea of troubles."

Personification appears in this line in Act IV, scene 1:

“Mad as the sea and the wind, when both contend/Which is the mightier."

The sea and the wind are here being personified as two angry men fighting to see which is stronger. This is an example of personification because the sea and wind are given human attributes of anger.

Here is one metaphor from Act I, scene ii: 

"This world...tis an unweeded garden, that grows to seed; things rank and gross in nature possess it merely."

This metaphor compares the world, the court of Denmark, to an unweeded garden, thus characterizing it as a corrupt place, overgrown with 'weeds' (courtiers and possibly murdering uncles) that contribute nothing and choke out what is good and fruitful.

In Act I, scene ii we meet another metaphor: Here Hamlet uses the metaphor of his flesh melting into a dew to describe death. This expresses his wish at that death would be a form of disappearing, of nothingness, that would take away his pain. Later, thoughts of an afterlife in hell will disturb this pleasant image of dissolving:

O, that this too too solid flesh would

melt

 Thaw and resolve itself into a dew