The outcome of the fight that pretty much ends the play is that everyone dies. Or at least Hamlet, Laertes, Gertrude, and Claudius all end up dead.
Gertrude is the first to die. She drinks from the cup of wine that Claudius has poisoned. It was meant for Hamlet, but Gertrude drinks from it first.
Then Claudius dies next. Laertes tells Hamlet that Laertes' sword was poisoned and that Claudius was responsible. Hamlet stabs Claudius with the sword and makes him drink the rest of the poisoned wine.
Laertes and Hamlet then die from the poison that was on Laertes' sword.
As William Shakespeare's Hamlet is a tragedy, the fight scene at the end of Act Five ends in the tragic deaths of almost all major characters.
Osric, a courtier, comes to Hamlet to tell him of a wager between Laertes and Claudius; Claudius believes that Hamlet could beat Laertes in a fencing match. Hamlet decides to engage in the match, not knowing that Claudius has plans to poison the victor's cup and that Laertes is fighting with a poison-tipped sword. After Hamlet strikes Laertes in the duel, he declines to drink from the cup. Hamlet's mother, Gertrude, sips from the cup and dies from the poison. Hamlet manages to take Laertes' sword from him and wounds the man, resulting in Laertes' death. In his great act of revenge, Hamlet stabs Claudius with the poisoned sword and forces him to drink the rest of the poison from the cup. Hamlet himself also dies, having been previously struck by Laertes' poisoned sword.
The scene concludes with Fortinbras and his army arriving at the castle, with Hamlet's dying wish being that Fortinbras be made the King of Denmark. Horatio promises to carry on the story of this tragic end, and Hamlet's body is removed from the hall.