"Hamlet" is a revenge tragedy: and as you'll see below, revenging one's father is one way Shakespeare structures the story. As a metaphor, you might argue that avenging one's father (and preserving the honour of the male line) stands for the growing up process, for becoming an adult man, or more simply for asserting one's own manhood.
1) Claudius murders Old Hamlet, Hamlet's father, by poisoning him in the orchard before the play begins. Hamlet returns from Wittenberg, and throughout the play, is determined (though he does not succeed until the final scene) to avenge his father's murder.
2) Old Hamlet killed Old Fortinbras, Fortinbras' father, in combat on the ice, before the play begins. Fortinbras returns to Denmark in order to avenge his father's death and reclaim the lands his father lost to Hamlet's father. In the end, he doesn't have to kill anyone - the entire Hamlet family are dead when he arrives.
3) Hamlet kills Polonius, Laertes' father, through the arras, in Act IV. Laertes returns from France to Denmark in order to kill Hamlet and avenge his father's death. He does so in the dual scene by means of a poisoned dagger: though he too dies from the venom.
1) Throughout the play, Hamlet seeks revenge against Claudius for the murder of Prince Hamlet's father, King Hamlet. He succeeds in his desire to kill Claudius in the final act of the play, but dies in the attempt.
2) Laertes seeks revenge against Hamlet for murdering Laertes's father, Polonius. He succeeds in killing Hamlet with a poisoned sword in the duel scene but in the attempt is also poisoned and dies.
3) After watching 'the play' Claudius realises Hamlet is too dangerous alive. He conspires to murder him by sending him to England with Roz and Guil. The plan backfires and Hamlet returns to Denmark unharmed. (some might say this was not revenge but cold calculating political murder)
4) Hamlet discovers that Roz. and Guil. are taking him to England with a letter which tells the English king to execute Hamlet, he takes revenge by switching the letter for a similar one which tells the English king to execute Roz. and Guil. R+G, unaware, deliver this new letter to the English king and are executed.