Were Hamlet and Laertes justified in their quests for vengeance?

Yes, absolutely! Hamlet's father was murdered in cold blood by Hamlet's uncle, his father's own brother, so that Claudius could take not only the king's crown and status, but also his wife. Worse yet is the fact that Claudius murdered his brother before his brother had an opportunity to confess his sins and be absolved, and so he was sent to Purgatory, a place of pain and suffering where he might be purged of his sins so that he can go to heaven. If Hamlet were not outraged and desirous of revenge, he would not be able to count himself a true or loyal son.
The father of Laertes, Polonius, was likewise murdered. Although Polonius is demonstrably less innocent than old Hamlet had been -- he was killed by Hamlet while he hid behind an arras in Hamlet's mother's bedroom -- he was still wrongfully killed nonetheless. He did not deserve to die; he was not a criminal as Claudius is. Moreover, he was not given any sort of significant honors after his death, and his funeral was rushed and his demise hushed up in a way that seemed to confirm some wrongdoing. Therefore, Laertes is likewise justified in his desire for revenge.