Presence

R. Gottleib mentioned a Medrash that ties together the "asher karcha bah'derech" form Parshas Zachor with something from the Megillah, the basic thrust of which was that Mordechai was communicating to Esther that Haman was from the long line of evil-doers known as Amalek. The Maharal explains the connection as explicating that the nefraiousness of Amalek lay in the fact that their actions were illogical, unassociated with any rational motivation. There attack on the children of Israel in the desert was not spurred on by expectations of wealth or yearnings for revenge, it was simple done out of abject hatred.

I would suggest a slightly different explanation, having not seen the Maharl in question. The magnitude of the evil in the actions of Amalek lie not in some sort of preternatural anti-Semitism, but in the arbitrary and capricious nature of their violence. God's eternal battle is not simply against those that start up with the children of a particular family of sheep herders, but against those that would create a world filled with random injustice.