history - What has the Holocaust taught us as a people?

The Holocaust was one of the most horrific and important events in our history. What have rabbis said are lessons we should take from it?

I am looking for lessons that should apply to all Jews, particularly those that should apply to our lives and outlook. References to notable speeches or documents addressing this topic would be a welcome addition to any answers, as I'm looking more for consensus or "generally notable" answers (such as from rabbis of major influence), rather than individual opinions.

Answer

The Lubavitcher Rebbe said to many survivors that from the Holocaust we see that one cannot rely on human feelings of morality. Until the Holocaust, many thought that the more cultured one was, the more intellectual one was, the more moral one would be. With the Holocaust, the entire Modern Western culture was shown to false. Scientists and Musicians either watched or actively participated in mass murder.

http://www.chabad.org/library/article_cdo/aid/64888/jewish/The-Rebbe-on-the-Holocaust.htm