Ok, as promised: for general overviews Paxton as said earlier is very good, there are a few other standards that people usually point to - Stanley Payne's A History of Fascism 1914-45 and it is very precise in what it considers fascism (Italy and Germany being the only two fascist regimes ever) but falls down on relying too much on a definition of fascism authoritarian national+vitalist macho military elitism. The last section on Interpretations of Fascism is really useful.
Another one often mentioned is Roger Griffin's The Nature of Fascism that shares common themes with Payne (rebirth of the nation) - and is the source for very widespread def of fascism as "a political ideology whose mythic core in its various permutations is a palingenetic form of populist ultra-nationalism." - but unlike Payne who uses the national rebirth idea to limit fascism to a particular era (whilst arguing later regimes utilised elements of original fascism) Griffin uses it to see it bloody everywhere and makes almost every area of political or social life forever open to study as part of fascist studies - the result is a flabby academy friendly heap of never ending words circling back on themselves (not Griffin - he's well worth reading, but the people who follow his approach). The popularity of both of these books may have something to do with their non-radical nature and their refusal to mention capital beyond there being 'economic circumstances' that radicalised people and movements.
Other examples of these big book are Roger Eatwell's Fascism: A History (flat and boring), Walter Lacquer's Fascism: A Readers Guide (v good if in need of updating in some places). And thousands of useless lightweight ones that say ww1-->inflation-->nazis blah blah blah
Right, onto what happened. For Italy by far the best one is Adrian Lyttleton's The Seizure of Power: Fascism in Italy 1919-29. For Germany Richard Evan's three volumes (The Coming of the Third Reich, The Third Reich in Power and The Third Reich at War) are unbeatable, esp if read with Ian Kershaw's fantastic two volume Hitler Biography (Hitler 1889–1936: Hubris and Hitler 1936–1945: Nemesis). The other utterly essential book is The Wages of Destruction: The Making and Breaking of the Nazi Economy by Adam Tooze - published in 2006 which overturned decades of lazy history. A shorter intro is The Rise of Fascism by F.L Carsten (who also did key work on the revolutions in central Europe at the end of WW1 that are directly connected to the rise of fascism). Can't go wrong with them as your basis.
Life in Nazi Germany: The Brown Plague: Travels in Late Weimar and Nazi Germany by Daniel Guerin (anarchist-communist author of the classic but outdated and simplistic Fascism and Big Business), A Social History of the Third Reich by Richard Grunberger, Life in the Third Reich ed by Richard Bessel - some really important essays in this collection (see also his essential Germany After the First World war, as there are in Nazism and Social Life 1933-45 ed by David F Crew. Hitlers's Social Revolution: Class and Status in Nazi Germany 1933-39.
Now the critical stuff, two books you have to read if you want to come at this from anything beyond a bad man came to power because germans were angry at a harsh Versailles treaty blah blah stuff: Social Policy in the Third Reich: The Working Class and the 'National Community' and Nazism, Fascism, and the Working Class by Tim Mason. Mason develops a model of the nazi state being pushed forward by its internal relations with the w/c (weak state, tottering and fearful of another upsurge of w/c opposition on the economic ruining it's longer military plans) rather than by external international relations which is the usual top-down approach to war and related issues. Tooze was very influenced by Mason. In the same ball park, Nazism and the working class Sergio Bologna and Karl Heinz Roth's The Other Workers Movement (if you read German).
Other works that undermine the crude ideas of how nazi Germany functioned and how people reacted to the various initiatives and so on (i'll leave aside open resistance until later) Inside Nazi Germany : Conformity, Opposition and Racism in Everyday Life by Detlev Peukert (his work on Wiemar is indispensable as well) and a couple of really good ones from Kershaw Political Opinion and Political Dissent in the Third Reich and The 'Hitler Myth' Image and Reality in the Third Reich, same area but with different more depressing conclusion is The Third Reich: Politics and Propaganda by David Welch.
How did Fascism and Nazism function: The spirit and structure of German fascism by Robert A. Brady, Behemoth by Franz Neumann and The German dictatorship;: The origins, structure, and effects of national socialism by Karl Dietrich Bracher, Economy and Class Structure of German Fascism by Alfred Sohn-Rethel.
Resistance: Communist Resistance in Nazi Germany By Allan Merson (to be read with the Ben Fowkes book Communism in Germany under the Weimar Republic - not very good but need it to get the later stuff), Eve Rosenhaft's Beating the Fascists?: The German Communists and Political Violence 1929-33 Political Violence, Political Violence in the Weimar Republic, 1918-1933: Fight for the Streets and Fear of Civil War by Dirk Schumann. Other resistances are looked at in Contending with Hitler. Varieties of German Resistance in the Third Reich - ed, David Clay Large, The German Resistance to Hitler, Graml, Mommsen, Reichardt and Wolf and German Resistance to Hitler by Peter Hoffman, Resistance Against the Third Reich 1933-1990, ed by Michael Ceyer and John W Boyer, Women in the Resistance by Margaret L Rossiter. Couple of interesting autobiographies as well - there are loads more, but i like these two - One Life is Not Enough: A German Woman's Anti-fascist Fight by Lore Wolf and The Darker The Night, The Brighter The Stars by Friedrich Schlotterbeck, Len Crome wrote a great book Unbroken: Resistance and Survival in The Concentration Camps about his Jewish communist brother in law Jonny Huttner. Haven't bothered with the aristocratic and elite 'resistance' - fuck 'em.
Radical interpretations: Marxists in The Face of Fascism ed by David Beetham (collection of contemporary documents, mostly 3rd international stuff, interesting to see what they thought they could see, how wrong they usually were). Radical Perspectives on the Rise of Fascism. The rather weak and cliched left-wing view can be found almost whole in The Nazis, Capitalism and the The Working Class by Donny Gluckstein - flimsy at best. The Tim Mason etc stuff is far better at being radical without needing to be stupidly polemical.
Interpretations: The Nazi Question: An Essay on the Interpretations of National Socialism (1922-75), not really an essay but a rambling book (in the french style) with some really interesting stuff. The Nazi Dictatorship: Problems and Perspectives of Interpretation By Kershaw (recommended). Reevaluating the Third Reich ed by Thomas Childers and Jane Caplan (reminds me, the formers The Nazi Voter is very important). Explaining Hitler's Germany: Historians and the Third Reich by Hiden and Farquharson and Hitler's Germany: Origins, Interpretations and Legacies by Roderick Stackelberg are two great ones for getting up to date with the general picture of research today before diving into the research itself. There is also a mass of stuff about the 'historians debate' in the 80s but i think that takes us past what we need really - but if anyone is interested the best start points are In Hitler's Shadow: West German Historians And The Attempt To Escape From The Nazi Past by Richard Evans and The Unmasterable Past: History, Holocaust, and German National Identity by Charles S. Maier
The Holocaust/Judeocide. First, what happened? Martin Gilbert's the Holocaust tells you almost day by day, but has little or no interpretative framework, it's almost a medieval chronology. Raul Hilberg's The Destruction of the European Jews first published in the early 60s is still standing. Absolutely essential. As are Saul Friedlander's two volumes Nazi Germany and the Jews: The Years of Persecution, 1933-1939 and The Years of Extermination: Nazi Germany and the Jews, 1939-1945. How it happened: The Origins of the Final Solution: The Evolution of the Nazi Jewish Policy 1939-42 by Chris Browning, Holocaust: The Nazi Persecution and Murder of the Jews and The Unwritten Order: Hitler's Role in the Final Solution both by Peter Longerich are central to modern debate. Why it happened: Kershaw's: Hitler, The Germans and The Final Solution is (as all his work is, excellent), Why Did the Heavens Not Darken? The "Final Solution" in History by Arno J Mayer is a must read, as is The Ideology of Death By John Weiss. Yehuda Bauer has a really interesting collection called Re-thinking The Holocaust, that i have many problems with but is still worth the read, so is Reading the Holocaust by Inga Clendinnen, despite it's non-historians approach.
I've tried to only recommend books that i personally found useful and that i know are influential and important in the field, and only a handful for each group - there are so many works on this it's unreal. I was going to go through my articles as well, but there are thousands of them - i'll try when i get some more time. I'll upload them all either way. I'll also steadily go through and re-edit this post to include links to most of the books.