Unfortunately, almost all my books on comprehensive German history are in German, which I suppose you don't speak? Two English Language books I can definitely recommend as "starters" that are both, reasonably rich in detail and engagingly written (at least to me) are: Christopher Clark's Iron Kingdom: The Rise and Downfall of Prussia, 1600-1947 and Fritz Stern's Five Germanys I have known.

Clark manages to pack the history of the state of Prussia into well under 1000 pages without rushing through its sometimes seemingly contradictory developments at unnecessary speed, glossing over important aspects/characters, or arranging history in a way that ends up presenting the eventual fate of Prussia - abolition by the Allies in 1947 and the stigmatization of being "the bearer of militarism and reaction in Germany" - as a forgone conclusion. His sources are many, varied and from what I remember a nice mix of both English and German works, so there should be some nice pointers for further reading to be found in the notes as well.

Stern's book is not a "straight-up" history book per se, but a sort of amalgamation of a history of Weimar to post WWII modern Germany and the family history of its author, the renown German-Jewish emigre and American historian Fritz Stern. If you are already well-versed in German history between the 1920s and, say, reunification in 1990, Stern's book will hold little news for you - but one thing I found him describe better than any other non-German I've read on the matter is the historiographical aspect. The way German Society (he chiefly uses the academic debate of German historians) dealt with Nazism after the war. He describes the different viewpoints and shifts in focus and interpretation over the decades, from the immediate post-war period, through the 1960s that brough us the Fischer Controversy, the 1980s Historians Dispute, to Daniel Goldhagen's "Willing Executioners" in the 1990s. It's a terrific insight into the mindset of the modern German nation and helps explain why Germany is so fiercely self-reflective and arguably bases all its political actions (or the conscious lack thereof) today on how it must not allow its own past mistakes to be repeated.

One more thing I would definitely urge you to check out, although it isn't a book, is the series of Podcasts by British Museum director Neil MacGregor called "Germany: Memories of a Nation". Those started out as a daily segment on BBC radio that ran last fall, which in turn were an addition/advertisement for an exhibition on the history of Germany at the British Museum. Each episode focuses on one or two artifacts that are representative of some aspect of the history of Germany. Objects range from state-of-the-art medieval craftsmanship items that were made in cities that back then were undisputably 'German' but don't belong to the modern Federal Republic anymore, over Dürer's protraits and how those images relate to 'the German soul/self-image' to the Bauhaus cradle's functional design and the hidden subversive message of Buchenwald Concentration Camp's gate. As diverse and unrelated as those sound, McGregor manages to elucidate how all are small parts of a general "German" history. The podcasts are free of charge, and the objects are prominent enough that a simple google search will always get you the correct corresponding pictures to look at while listening. Keep in mind that the series is best enjoyed chronologically, so start at the bottom of the page I linked you to (View from the Gate, Sep 29th). To the best of my knowledge, there is also a recently published book on the series - I haven't gotten my hands on that one so far, so I can't comment on whether it might be inferior or superior to the podcasts, or simply make a nice addition. One thing I CAN say for the podcast, however: the use of music in some of the episodes, together with the narrative, is so powerful that it repeatedly had me in tears while listening - and I would categorize myself as a genreally pretty jaded person, at least in regards to the emotive effect of German history.

The professional historians will give you enough recommendations of scholarly literature, I would hope. On the odd chance that you may additionally be also looking for light-hearted popular treatments of the subject, I will say I greatly enjoyed (as a layman whose only qualification is being German :-) Simon Winder's "Germania". His Brysonesque, droll, slightly coffee-tablish account of German history from 9 CE to 1933 is not without its problems (and if you google for reviews, from the Guardian to the WSJ, you will find that most reviewers have addressed these problems in what strikes me as an unusually fair and helpful manner), but it is still a good read.

And if you are into the intangible, spiritual world of "ideas" (something mostly absent from practically-minded Winder, even though it is so quintessentially German), you may enjoy the slightly experimental "1913 - The Year Before the Storm" by Florian Illes. To be fair, it does travel around a bit, from Spain to Italy and beyond, and looks at French artists and Russians, etc., but always through a rather German lens, and with a German's eye for what tickles the philosophical fancy of Germans. Of course not a serious history book, but I'd say it does an excellent job in recreating how 1913 must have felt to contemporaries (at least in literary and artistic circles).

The book Rite of Spring by Morris Eksteins is a really good book to read for the general perspective of society in europe (not just Germany) during the time just before the world wars. Its a bit of a harder read, but very rewarding.

For the long 19th century, I'd highly recommend this book. It is very readable and covers many topics:

Blackbourn, David. History of Germany 1780-1918: The Long Nineteenth Century. 2nd. Ed. Malden, MA: Blackwell Publishing, 2003.