How does Shakespeare present the theme of remembrance in Hamlet?

This theme runs throughout Hamlet from his first famous soliloquy, in which he jabs at himself, "Heaven and earth!/Must I remember?" when recalling his father and how he behaved towards his mother and in his words to Horatio in which he describes seeing (remembering) his father in his "mind's eye," to the Ghost's own words, "Adieu, adieu, remember me."
Many other characters cite memory as well, as in the final interchange with brother and sister Laertes and Ophelia:
LAERTES
Farewell, Ophelia; and remember well
What I have said to you.
OPHELIA
'Tis in my memory lock'd,
And you yourself shall keep the key of it.
Hamlet "remembers" a great deal of a speech he heard the Players recite and quotes it from memory, and just after his most famous soliloquy, "To be or not to be," he sees Ophelia and says, "Soft you now!/The fair Ophelia! Nymph, in thy orisons/Be all my sins remember'd." (Note that "orisons" means "prayers.")
The play continues to weave the theme of remembrance throughout its course, showing how difficult it is for human beings to let go of the past. Hamlet remembers his own childhood in the gravediggers' scene:
"Alas, poor Yorick! I knew him, Horatio: a fellow of infinite jest, of most excellent fancy: he hath borne me on his back a thousand times; and now, how abhorred in my imagination it is!"
Does Hamlet's preoccupation with reliving the past prevent him from "sweeping to his revenge" as he promises to do in act 1? That is a question that each production, each director, and each actor playing Hamlet have to answer anew each time the play is mounted.