There are so many universal themes in Shakespeare's play Hamlet, and all of his plays, which is why I think they tend to stand the test of time so well.
Alienation is a good one. Here are two more that I can think of off the top of my head, along with a brief explanation for each:
Passion v. Reason: To me, this is the most prominent theme at the forefront of this play, and I think it is most articulately shown in Hamlet's famous "To Be or Not to Be" soliloquy. Hamlet's internal struggle throughout the entire play is whether or not he should take action at any given point. He gets so caught up in reason, that he fails to act at a number of opportune moments, the most famous being Act III, Scene iii, where Hamlet catches Claudius in confession but does not take his revenge. Other times, Hamlet is ruled by his passion and does not stop to think twice about what he is doing or saying to other characters. This is most apparent when he stabs Polonius. This theme comes up in many other texts, including other Shakespeare tragedies.
Loyalty: This is another major theme in this play. Throughout the play, Hamlet judges all of the other characters based on their loyalty toward him. Horatio, for example, he feels has been tested by Claudius and remains loyal. He is the only character Hamlet can trust. Ophelia and Rosencrantz and Guildenstern both prove disloyal when they promise Claudius they will find out what's bothering Hamlet and report back to him. He views Gertrude as disloyal from the start because she has married his father's brother so soon after Old Hamlet's death. Meanwhile, Hamlet's main conflict over seeking revenge in the first place is rooted in his desire to remain loyal to his father. Loyalty is also a major theme in other Shakespeare plays (Romeo and Juliet, Othello), as well as other non-Shakespearean texts.
I will also include some links at the bottom from this site that will help answer your question as well.