Gertrude murdered Ophelia.She seems to know an awful lot about Ophelia's death - before, during and after it happened. She also doesn't seem that upset. Hmm.
Hamlet is Claudius's illegitimate son, and Hamlet is one of the few people at court who doesn't know it.
Hamlet is a robot.Built by Hamlet Sr., he struggles to understand humans.
Ophelia is pregnant.Not so much WMG as very strongly hinted...
Horatio is making this whole thing up.He actually killed everyone. Possibly driven mad by all the angst.
Horatio is a spy for Fortinbras.He has been secretly manipulating things at court to make Fortinbras's takeover smoother. He pretended he was going to drink the poison because he truly liked Hamlet and wanted Hamlet to still think of him as a friend before Hamlet died. This leaves Horatio alive at the end to report to Fortinbras everything that has happened.
Hamlet and Horatio are lovers."Give me that man / That is not passion's slave, and i will wear him / In my heart's core, aye, in my heart of hearts / As I do thee. " - Act 3 Scene 2, 71-74 This wayward passion if of course not appropriate for a prince. But the anxiety of being closeted with his love serves as a major source of his anger and melancholy.
Ophelia was visited by the ghost of King Hamlet after Polonius died.On that note, said ghost is an Eldritch Abomination who drives whoever it talks to to insanity. That's why it refused to speak to the guards. Lastly, Ophelia realized that the ghost planned to throw Denmark into ruin, so she committed suicide so she wouldn't be a part of it.
The ghost is a hallucination, not the actual spirit of King Hamlet.It doesn't speak to anyone except Hamlet, and when it does, it doesn't really give him new information. In fact, it tells him exactly what he wants to hear — his reaction is even "I knew it!" Also, not only is it the only character other than Hamlet to label Gertrude and Claudius' marriage as "incest", it actually seems more passionate and vehement about that topic than the whole, you know, murder thing. If it was really the ghost of Hamlet Sr., wouldn't he be more concerned with his brother killing him than his brother marrying his wife (as was standard practice back then)? Hamlet's the one with the "incest" hangup, so the only way this makes sense is if the ghost is a reflection of his own neuroses! And of course, Gertrude can't see the ghost, which is highly suspect given that the ghost is telling Hamlet to take mercy on her in that scene — why wouldn't it show itself to her? As for the guards, they never appear again after act 1 scene 2. Who's to say they aren't hallucinations either, made up by Hamlet to rationalize the ghost's appearance?