Hamlet:  The star of the play.  Hence, the name of the play.

Ghost:  Ghost of Hamlet.  No, not the star of the play.  This is a bit confusing, so listen close.  Hamlet (the star) is the Prince of Denmark.  The ghost is Hamlet, former King of Denmark.  Father and son share the same name.  Hamlet is Hamlet's father.  Or, Hamlet is Hamlet's son.  Confusing, no?

Claudius:  The new King of Denmark.  Brother to the dead Hamlet, uncle to Prince Hamlet.

Gertrude:  Queen of Denmark.  Was married to King Hamlet, now married to King Claudius.

Polonius:  Councilor to the King (Claudius).  Or, in more familiar terms, he's Claudius's right hand man.

Ophelia:  Polonius's daughter.  Laertes's sister.  Also Hamlet's girlfriend.

Laertes:  Polonius's son.  Ophelia's brother.

Reynaldo:  Polonius's servant.

Horatio:  Hamlet's friend and fellow student.

Members of Danish court:  Voltimand, Cornelius, Rosencrantz, Guildenstern, Osric, A Gentleman, A Lord

Officer's and Soldiers on watch:  Bernardo, Francisco, Marcellus

Fortinbras:  Prince of Norway

Catain: in his army.  (don't ask, not important)

Misc. nobodies.