1. The first key passage would have to be when Hamlet realizes that Ophelia is dead. This is when he comes out from hiding and admits to everyone that he loved Ophelia. Also, Laertes and Hamlet have their little fight and this is very important. It sets the tone for how the rest of the play is going to turn out. Now, Hamlet is back and the king and Laertes have to act on their plan to kill Hamlet.
2. The second key passage is when the queen drinks from the poisoned cup and Hamlet and Laertes are both now injured. This passage is basically the end of the play. Now we can pretty much tell that they are all going to die. But, before they die, Laertes realizes that the king was the bad guy all along and he tells Hamlet that and Hamlet kills the king. This ties the whole play together and brings everything to an end.