"Remember what the Amalekites did to you on the way, when you left Egypt. They met you along the way and attacked the weak members of the nation at the back of the pack, and you were exhausted. They did not fear God... And it will be, when God gives you rest from your enemies round about, in the Land that God has given to you as an inheritance, you are mandated to wipe out the memory of Amalek from beneath the heavens - Do not forget!" (Devarim 25:17-18)
The mitzvah to remember the evil deeds of Amalek is not an obligation to merely remember that nation's actions, but to recall that we have an obligation to blot out the memory of Amalek. There are those for whom this mitzvah is difficult to accept; their humanistic leanings have a hard time grappling with such a commandment...
We have witnessed this kind of attitude in the past, as the sages say in Tractate Yomah (22b) "When God say to King Saul: 'Go and wipe out Amalek,' Saul said: 'For the murder of one soul, the Torah required the [intricate ceremony of] neck-breaking of a heifer, ['Eglah Arufah']. For all of these souls [that you have instructed me to kill] how much moreso would [such atonement be required!]' And even if human members of that nation sinned, in what way did the animals sin [that I should be obligated to kill them?
And if the adults sinned, what did the children do to deserve death? A Heavenly Voice descended from on High and said: 'Don't be too much of a Tzaddik (Righteous person)"'.
It was because of this attitude that Saul lost his position as King of Israel, because he acted compassionately to Agag, King of Amalek and did not kill him. Compassion towards the wicked is really wickedness. Because of Saul's misplaced compassion, our sages tell us, the evil Haman- a direct descendant of Agag - was nearly able to exterminate us.
It is along these lines that Rabbi Levi opened his speech in honor of Purim: (Talmud, Megillah, 11a): "If you do not uproot the inhabitants of the Land, and allow them to remain - they will become thorns in your sides, and will cause trouble for you in the Land in which you dwell." (Bamidbar 33:55) This verse is speaking of King Saul, and of his error in sparing Agag.
The mitzvah, then of wiping out Amalek, actually stems from the value of compassion and kindness - compassion on all those whom Amalek threatens to exterminate. This mitzvah is an ongoing one, and valid even today. The cursed Nazis were the spiritual heirs of Amalek. They did not just want to exterminate us; they succeeded in actually murdering many millions of our people, a full-one third of the world's Jews! Today, too, there are those - driven by a deep-seeded anti-Semitism - who desperately wish to kill us. These are the people whom the Torah commanded us to obliterate, to leave no memory of them...