I'll assume that you're open to anything, so one book that you might enjoy was David Blackbourn's The Conquest of Nature, and environmental history of Germany since the 18th century. He deals with a range of topics from an environmental perspective, including draining marshlands in northern Germany, management of the Rhine, and the complex relationships between Nazi ideology and ideas of nature. He's very good at demonstrating the intimate connections between ideas of nature and its management and broader trends in German (and European) history, so it's not like this is some cottage-industry, irrelevant, fringe bit of scholarship. I'm sure that specialists in German history could offer works that make different interpretations, but Blackbourn's work is well-written, he's a respected scholar, and this is not a bad place to start.

If you've got any interest in Prussia and how it came to dominate Germany, Iron Kingdom: The Rise and Downfall of Prussia, 1600-1947 by Christopher Clark is a great book.

What time frame are you looking for, just a general history?

On the 30 Years' War, Europe's Tragedy by Peter H Wilson

If you want to go with an actual German historian, have a look at Winkler's Germany: The Long Road West. It's a classic, although his sonderweg argument is quite controversial.

I second the recommendation of Hagen Schulze. It's probably the best quick introduction to German history.

I will think about some more and edit my post later

Very detailed surveys of 19th and 20th centuries:

James Sheehan, German History 1770-1866

William Carr, German History 1815-1990

I'd suggest 'The Third Reich' by Michael Burleigh if you are interested in that period.

Depends on what time period you're talking about, but if you're interested in the first half of the 20th century, these two books are worth a look.

Berlin in Lights

Chosen as a New York Times Notable Book, is the collection of German aristocrat Harry Kessler's diaries between the two world wars. Count Harry Kessler (1868-1937), the son of a German banker and an Irish beauty, was a diplomat and publisher who moved easily among the worlds of art, politics, and society. He lived in Berlin but traveled throughout Europe, always with a keen eye to the political climate of the times.

http://books.google.com/books/about/Berlin_in_Lights.html?id=y_BJt918BHoC

Before the Deluge (can not recommend this book enough)

This evocation of the figures and events of one of the most extraordinary eras of this century makes "the most vivid portrait of the period yet written . . . The culture is plentiful and the gossip is spicy" -Time

http://books.google.com/books/about/Before_the_Deluge.html?id=K6u0eLY4FooC

Although it's very long in the tooth, Gordan A. Craig's The Germans is an accessible and insightful examination of various aspects of German society and culture (gender, literature, money, the language). Craig was a graduate student in Germany in 1935 and his perspective on Germany is tinged with the question could the Federal Republic go the way of Weimar (Craig ultimately answers in the negative). Even though the book is quite old, it still has a valuable perspective.

One of the more inescable elements of contemporary Germany is the salience of the past for many Germans today. For a more academic view of German memory culture, Rudy Koshar's From Monuments to Traces: Artifacts of German Memory, 1870-1990 is an excellent and elegant survey of German memory culture and how various iterations of memory have reflected the complex relationship Germans have with their past.

Kleine deutsche Geschichte - Hagen Schulze

Just a brush over German history for starters...nothing in depth. Plus it's in German (not too complicated), so it might help learning the language.

Arms, Autarky and Aggression: A Study in German Foreign Policy, 1933-1939 by William Carr is short and awesome. It's out of print, but try to find a copy.