For me personally one of the biggest events in 3+ years of ebook reading was the opening of Amazon.de a couple of weeks ago, and it has implications for anyone who reads German anywhere. In anticipation of the opening, Amazon began working to improve access to public-domain material in German (and is clearly taking parallel steps in the run-up to the launch of its French Kindle shop). I spent hours yesterday going through free German-language offerings at Amazon.de and Amazon.com and came up with links to significant ebooks that you would have been hard pressed to find at any price a few months ago. (I'll propose some comparable links to material in English and French in other posts, especially as the French-language selection improves. Today's links are all to Amazon.com, i.e., for U.S. and international use; if anyone wants the corresponding links to Amazon.de, please message me via Facebook [badge in right-hand column of this blog].)
It's long been possible to find German-language literary classics, especially the older ones, on the Internet, e.g. at Gutenberg. Here are new options, often for harder-to-find material, all of it 'nonfiction'. (My apologies for 'disappearing' material and any broken links.)
Where, realistically, might a person start reading Hegel? Consider the theoretical introduction to his lectures on the philosophy of history, the introduction popularly known as 'Reason in History'. Digital offerings of Hegel used to be sparse or expensive: yesterday the Vorlesungen über die Philosophie der Geschichte were free but today they are not to be found. I suggest you try another search in the future... or go with 'the big one', Phänomenologie des Geistes. [UPDATE 12 June 2011: The Vorlesungen über die Philosophie der Geschichte are now back in the Amazon database and are currently free.]
And Marx? In the strange absence of a German ebook edition of Das Kapital, consider either one of the multiple free editions of the Communist Manifesto or my pick (made available last year as an ebook but only now for free), the Ökonomisch-philosophische Manuskripte (also known as the Paris Manuscripts) of 1844; best known for their development of the theory of alienation, they are the cream of the young Marx. [UPDATE 8 November 2011: Note that the full German text of all three volumes of Das Kapital is now available as an ebook--not free, but as a very reasonably priced ebook from Amazon.com or Amazon.de.]
Nietzsche's works published during his lifetime have long been readily available as ebooks (now free); his indispensable posthumous writings of the 1880s, best known under the titles Der Wille zur Macht or The Will to Power and often the victims of editorial error or distortion, were available yesterday in five free ebook volumes entitled Fragmente but have disappeared again. [UPDATE 12 June 2011: These, too, are now back in the database, and all five are currently free. Search Kindle books for nietzsche fragmente .] Consider instead the earlier posthumous fragment Über Wahrheit und Lüge im außermoralischen Sinne.
Freud is even more slippery, at least for now. The downloads that I would like to recommend (Die Traumdeutung and two case histories) are ineligible here because they cost 99 cents apiece. The most enduringly indispensable of the free options is probably Das Unheimliche, but, if you're looking for introductions to psychoanalytic theory for lay readers, consider Zur Psychopathologie des Alltagslebens and Über Psychoanalyse.
Kafka's novels and short stories have long been available as free downloads: surf his pages at Amazon.com and regale yourself. Don't miss this new free ebook, though, Tagebücher 1910-1923, or this old--is 'favorite' really the right word?--Brief an den Vater.
I found a single work by Georg Lukács among the free German-language ebooks, but it's a fundamental (pre-Marxist) one, Theorie des Romans (1916). (I suspect that there are few readers who will find themselves in perfect agreement with Lukács in any of his books, but the same may be true of most of the writers in this list--indeed, of most of the writers we find indispensable.)
Finally, Walter Benjamin entered the public domain only recently in most of the world. My sentimental pick of a Benjamin volume to recommend here is his anthology Deutsche Menschen, subtitled 'eine Folge von Briefen', compiled with commentary by Benjamin. There are other important Benjamin ebooks, especially for two or three dollars, but Deutsche Menschen is the sort of powerful document that comes along only once....