The "Saint Crispin's day" speech (you know, "We few, we happy few, we band of brothers").
The conquest of Harfleur, where Henry delivers a terrifying description of the havoc his soldiers will wreak on the town and its citizens if its leaders don't surrender. They do, and Henry promptly tells his lieutenant not to do any of the things he just said.
The Prologue itself. Quick summary in modern English: this story is so fantastic that I worry I can't do it justice; I wish I had the world for a stage, gods as actors, armies of extras, and monarchs as an audience—but all I have is this little band of actors in a little wooden theater, so I humbly ask that you use your imagination to fill in the rest.