Is justice appropriately served to each character at the end of Hamlet?

I think justice is served appropriately to most characters by the end of the play. Claudius, who killed his brother and then married that brother's wife, is killed by a combination of the "envenomed" point of Laertes's sword and the wine that Claudius himself poisoned to ensnare Hamlet. Gertrude, who was faithless and married her dead husband's brother just weeks after her husband's death, is poisoned by the wine prepared by her husband to murder her son. Laertes, whose father Polonius was slain by Hamlet and who conspired with Claudius against Hamlet and put poison on the tip of his sword in order to slay Hamlet (a rather dishonorable act), is killed by this very poison when he and Hamlet switch weapons during the fight. Hamlet eventually dies as a result of his injuries with this same poisoned weapon; he did delay his revenge on Claudius to the extent that other innocent people died in the meantime, including Rosencrantz and Guildenstern, Polonius, and Ophelia. Rosencrantz and Guildenstern were Hamlet's friends from university who became unwitting spies for Claudius. They had no evil intent. Polonius worked for Claudius but did not share his malice for Hamlet; he seemed genuinely concerned about the prince's well-being and mental health. Ophelia seems to have gotten caught in the crossfire between Hamlet and Claudius, and she did not deserve to die.

Was justice served in Hamlet?

Another way of stating this question would be to ask, did the characters who end up dead at the end of the play deserve to die? In the broadest theological sense, Shakespeare would answer yes: in a Christian worldview, we are all born sinners, and for that reason, all of us pay the price by eventually dying. This is a question Hamlet explores in the play, both when he talks about humans fearing the afterlife (and so not committing suicide) and when he looks at Yorick's skull and notes that death is great leveler: every human, young or old, will die.

But, to be discerning, how do we specifically evaluate the crimes of the central characters? We can certainly say that Claudius deserved to die: he cold-bloodedly murdered to get the throne and felt no remorse. He also tried several times to have Hamlet murdered.

Hamlet killed Polonius, but that was an unpremeditated error. He also arranged for the deaths of Rosencrantz and Guildenstern, but we could (perhaps) call that self-defense. He showed no remorse over any of these deaths, which is more troubling. He made some mistakes but probably didn't quite deserve to die, as he was driven to desperation. But this is arguable: you need to think about it.

Gertrude seems to have married a man she didn't love simply to secure her own safety and stay on the throne. Is that the best reason to marry? No. Does it deserve death? No.

Laertes comes home ready to kill Hamlet to avenge his father's death and willingly participates in the plot to use a poisoned rapier against Hamlet. However, he repents of his hotheadedness. He, too, probably doesn't deserve to die. Given a little time, he would most likely have come to his senses.

"Justice" went a bit overboard at the end of the play, and therefore, the ending wasn't entirely just. But all the deaths satisfy the requirements of the revenge drama, and they do clean house and allow for a new beginning.