A king can be defined as one who protects his land and people. He should have qualities such as extreme intelligence (common and book), excellent fighting abilities, trustworthiness, and justice. He must be able to put aside personal differences and see what is best for his land. This is one of the most important qualities a king must possess, for “Kings are earth's gods; in vice their law's their will”1. Because of this quality Hamlet, would have been a good king, but would have to fight his wills.
Too many times did Hamlet hurt someone unrelated to get his revenge. Not only did he kill Polonius, but because of this Ophelia drowned herself. This also caused Laertes to die. Most critics blame Claudius for most of the deaths, but if Hamlet had not listened to the ghost, or had not had the amount of rage he did, then the people would not have been killed. However, Hamlet could have learned from these mistakes and seen that he cannot do whatever must to done to avenge someone.
Hamlet came from a line of Kings. He grew up knowing someday he would become king. He went to a school named Wittenberg, and wished to go back there at one point in the play. Hamlet spoke the one of the most famous lines in the English language, contemplating life and death, revenge and suicide. Hamlet's friends trusted him, even when he pretended to be mad. Therefore, Hamlet possesses royalty, intelligence, and rationalization, and his trusting friends show that he is trustworthy.
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Hamlet was a questioning man. He didn't trust things as they were right away. Part of this is from his education, but most of this comes from his upbringing in the castle. A king must be able to see a liar, for people will always try to deceive him. This is shown when Hamlet is on his way to England. He checks below the ship when he doesn't trust his Uncle. There he finds an order for his death.
He is also able to weigh his actions with the consequences. He thought himself out...