The culture blog Flavorwire had a good series recently on 10 of the Most Precocious Authors in Literary History, which, however, did not include one German writer. Since I love lists, I've created my own top five precocious writers - those whe were doing serious work before the age of 20. Of course, I use the term "German authors" loosely, since three out of the five are Austrian. Please add other names to this list in the comments.
Joseph Freiherr von Eichendorff (10 March 1788 – 26 November 1857) was perhaps the most precocious of the precocious group of Romantic poets. At the age of nineteen he wrote the poem Das zerbrochene Ringlein (In einem kühlen Grunde) where the themes and melodic style that would shape Eichendorff's poetry in the decades to come are already on full display.
Georg Trakl (1887 -1914) was nearly as precocious as his literary idol Arthur Rimbaud. His two one-act plays Totentag and Fata Morgana were performed in the Salzburger Stadttheater when Trakl was only 18. His most famous poems - with the exception of his last great war poem Grodek - were finished before he turned 25. His second collection of poems - Sebastian im Traum - appeared shortly after Trakl died from an overdose of cocaine in 1914.
Rainer Maria Rilke (1875-1926) didn't find his true lyric voice until he was able to leave Prague behind. But René (as he was called until he met Lou Andreas-Salomé in 1897) published his first collection of poems Leben und Lieder at the age of nineteen. His virtuosity is apparent in these early poems and in his Florenzer Tagebuch. Already he was wrestling with the same themes - the reconciliation of beauty and suffering, life and death - that he would much later capture in perfect lyric form in the Sonnette an Orpheus.
Hugo von Hofmannsthal (1874 - 1929) took literary Vienna by storm at the age of 16. His genius was such that he was stalked by Stefan Georg at his gymnasium. Stefan Zweig recalls young von Hofmannsthal in Die Welt von Gestern: "The emergence of the young Hofmannsthal is noteworthy as a miracle of early perfection: in the history of literature I can't think of any example - other than Rimbaud or Keats - of such mastery of language at a young age."
Bertolt Brecht (1898 - 1956) demonstrated his ambition to create epic theater at the age of 15 by writing and publishing a drama of the greatest epic story ever told - Die Bibel. He also showed early promise for agit-prop by writing antiwar pieces that nearly got him kicked out of school.