Disclaimer:
As I was made aware of this by Drux' comments: my answer may lead some people to believe that I am in some way justifying people not intervening, or even actively participating in the Holocaust.
If read the comments below, I hope it is self-evident that this is not the case.
Just to be clear: I absolutely and unequivocally condemn any action that discriminates on the basis of religion and or race, be it in the past, present or future.
My main interest, as far as history is concerned, is 20th century geo-politics. The question of how could this happen is one that we all ask about every genocide. What I tend to do (and attempted to do in my answer) is to shift that question to could this happen (again) today or is it happening again.
Of course, when attempting to apply this very sensitive subject (WWII genocide) to modern-day politics, I recognize the fact that bad choice of words or phrasing can lead to misunderstandings. It also stands to reason that a 1-on-1 "projection" of past events onto the present is, by definition false/flawed. But the cliché of history repeating itself is, IMHO, not all together absurd.
Anyway, it is not my intention to hurt people, I am not trying to negate or minimize any of the atrocities that were committed. My only goal is to communicate what I believe are genuine similarities between the rise of Nazi Germany and today's political tendencies/evolutions.
And to avoid any further misunderstandings, let's not beat around the bush: I have no sympathies towards anything even remotely resembling fascism or (neo-)Nazism whatsoever.
So if you are a neo-Nazi looking to recruit: try your luck at the local asylum, or try reading a book, instead of using it as a hammer.
If the contents of my answer below offends anyone for any reason, do not hesitate to leave a comment, and I'll be happy to clarify whatever needs clarification, or edit my answer in accordingly.
From the off: The phrase "Wir haben es nicht gewusst" is a lie. Many Germans have later admitted that the deportation and mass killing of Jews, Gipsies and political prisoners was a public secret.
At first, it could well be that not everybody was equally aware, and yes, the German economy was headed in the right direction, and yes the Nazi regime did manage to create jobs, and instill on the people a lost sense of pride. So it's not unlikely that, at first, people were willing to subject themselves and others to the nasty sides of the regime.
By the time the ghastly things that were going on had become this public secret, the Nazi apparatus had managed to infiltrate every aspect of daily life, though. There are recorded accounts of children that got sent home from school, and were expressly prohibited to attend classes until they joined the Hitler Jugend.
Though this does not serve as justification, with the rise of fascism, there grew a sense of terror among the population, too: if they didn't contribute, that was seen as a sign of rebellion, and thus they, too, could fall victim. But that's just one of many reasons why the Nazi's could keep on doing what they did, and does not answer your question.
For that, we need to go back to the end of WWI.
Germany had capitulated, and was heavily punished (Treaty of Versailles). WWI was in part caused by the Germans wanting a part of the colonial pie that the rest of Europe were having (among other things of course) as you may know.
While the Treaty of Versailles was said to be about making amends and repaying war damage to those countries involved, it also prohibited Germany to expand its borders (ie: no colonies).
Do not underestimate the social trauma a nation can sustain when, already having had to admit defeat, being forced to forego the perks (colonies back then were seen as a nations right) other countries so happily grant themselves.
A nation is a mass of people, and a mass behaves irrational and emotional (like a toddler). Tell a 3 year old it's done wrong, punish it and then tell it, it has to watch while other toddlers are eating its sweets, it'll cry, kick and scream.
So there was a genuine feeling of betrayal and disgruntlement in Germany. There had also been a long tradition of antisemitism in Europe. Couple that to the rise of Communism (Russian revolution happened during WWI) and you have: Anger, Fear (of Communism) and a not-well-liked minority. That's an explosive mix, no matter how you look at it.
All you need is a spark: a charismatic leader, preferable one that also manages to restore some of the national pride that the country in question seems to have lost.
An interesting read in this respect is "The Nuremberg Diary". Gustave Gilber, an American psychologist interviewed Hermann Göring and wrote their conversation down:
Why, of course, the people don't want war. Why would some poor slob on a farm want to risk his life in a war when the best that he can get out of it is to come back to his farm in one piece? Naturally, the common people don't want war; neither in Russia nor in England nor in America, nor for that matter in Germany. That is understood.
When you speak of WWII and the Holocaust in particular, it stands to reason that the same "rule" applies: the people aren't actively asking for pogroms. But Göring continues:
But, after all, it is the leaders of the country who determine the policy and it is always a simple matter to drag the people along, whether it is a democracy or a fascist dictatorship or a Parliament or a Communist dictatorship.
Leaders are indeed the ones that make out the policies, both domestic and foreign. It is they who stand to gain from conflict. Economic and geopolitical factors come into play, and quickly overtake humanitarian considerations. As far as the leaders of a country are concerned, human casualties become statistics, and are seen as part of the cost vs benefits analysis.
Basically, it's as Joseph Stalin (allegedly) stated:
A single death is a tragedy; a million deaths is a statistic.
All things asside, but in the interest of correctness, this may not be Stalin's quote
How about this one, by Jean Rostand:
Kill one man, and you are a murderer. Kill millions of men, and you are a conqueror. Kill them all, and you are a god.
Back to Göring, though, Gilbert points out a possible flaw in Göring's logic: the fact that a democratic society couldn't possibly elect a gouvernament that institutionalizes the prosecution of certain groups of people:
Gilbert: There is one difference. In a democracy, the people have some say in the matter through their elected representatives, and in the United States only Congress can declare wars.
Göring, however, does not see things like this, and actually summarizes the plot of Orwell's yet to be written novell 1984:
Göring: Oh, that is all well and good, but, voice or no voice, the people can always be brought to the bidding of the leaders. That is easy. All you have to do is tell them they are being attacked and denounce the pacifists for lack of patriotism and exposing the country to danger. It works the same way in any country.
In Germany, the people were brought to the leaders' bidding by first: creating jobs, improving the economy, breaking the Treaty of Versailles and reinstating the sense of National pride.
Targetting Jews and Gipsies was, in a way, self-evident: they could be the scape-goat and play the role of the enemy that has already infiltrated the country. They were seen as the ones that stole the wealth of the German people.
People are worryingly gullible when it comes to things like this as American schoolteacher Jane Elliott's infamous experiment has demonstrated time and time again. Here's a clip
There have been many experiments like this, and all of them seem to come to the same conclusion: When people are put in a situation where they feel they have the right to exercise power over another group, violence ensues, and is even seen as justifiable.
Ironically, a more recent example of this can be seen in Israel, and the way people treat muslim refugees. They aren't even referred to as refugees, but "Infiltrators", in the same way the Jews were seen as the enemy that lived within back in WWII Germany...
Even more worrying, though: this phenomenon is so inherent to human nature, we don't even notice it's going on all around us:
After 9/11, Bill Mahr caught some slack for saying the suicide attackers were not cowards. At the same time, Howard Stern stated that America should choose "any Arab country, they're all harbouring terrorists, and just nuke 'em". Bill Mahr was fired, Howerd Stern wasn't.
Look at the people who have used the quote: "You're either with us, or against us" in various forms here: Lenin (Communist), Mussolini (Fascist), George W Bush (US president), Hillary Clinton (US Foreign Secretary) and Vic Toews (Canadian public safety minister).
Since the Communist and Fascist dictators, the phrase has always been used in a context of threads to national security, mainly terrorism.
This threat is also used to justify mass surveillance, invasive searches in airport security, The patriot act (Christ, patriotism and (extreme) nationalism is in the name), active prosecution of whistle-blowers like Edward Snowden, and racial profiling.
Now think about these things, and read the quote by Göring a second time:
Göring: Oh, that is all well and good, but, voice or no voice, the people can always be brought to the bidding of the leaders. That is easy. All you have to do is tell them they are being attacked and denounce the pacifists for lack of patriotism and exposing the country to danger. It works the same way in any country.
How could something like the Holocaust happen, and could it happen again? I'm afraid to say that I believe it can happen anywhere, and if it were to happen again in our life-time, we wouldn't realize it before it's too late, and even so: few of us would actually have the courage to step up and do something about it.
A couple of books that are loosely related, in the sense that they touch on, or identify similarities between nazi- or communist dictatorships and current western foreign policies:
Gore Vidal: Permanent war for Permanent Peace
William Blum: Rogue State