and now with the boldface closed:

A Basic German Folksong Library

There are innumerable German folksong books of which I know only a small part and the best of those I know are below. It is a very personal choice and I add some remark to make clear what to expect in the unlikely case you should consider buying them. One of them, Steinitz, I once have donated to the Cecil Sharp Library (London) for their patience and kindness when I was there for days in succession. If it is still open to the public you should be able to see it there.
The 'must have' are in boldface (from a collector's point of view, the 'must have ' from a singer's point of view is the last entry).

L. A. von Arnim & C. Brentano, Des Knaben Wunderhorn (the lad's miraculous horn), orig. 1806/1808, many reprints, e.g. from DTV, 3 volumes, 1984.
notes: about 1500 songs without tunes, no explanation to the songs, at least in my edition
comment: an old and at that time very valuable collection, many of the songs not sung today

W. Steinitz, "Der grosse Steinitz", Deutsche Volkslieder demokratischen Charakters aus sechs Jahrhunderten (The big Steinitz, German folksongs of a democratic character from six centuries), 2 vol., East-Berlin, 1955, later reprints e.g. by Zweitausendeins, probably out of print today and very hard to find.
notes: about 300 songs not counting variants and parodies, no tunes, scholarly annotated
comment: the nearest I know to Child, edited in the GDR, therefore a predictable political bias with notable omissions, but a great book nevertheless

E. Klusen, Deutsche Lieder (German songs), Insel Verlag, 1980
notes: about 800 songs with tunes and annotations
comment: no bias whatsoever discernible for me, a great collection from the earliest known songs until today

H. Breuer, Der Zupfgeigenhansl (Johnny with a guitar), orig. 1908, many reprints until today by Schott Verlag.
notes: about 250 songs with tunes and chords; attention some reprints are in the original 'fraktur' writing (a page in Fraktur as an example) that makes reading difficult if you are not used to it.
comment: songs sung by the 'Bündische Jugend', the nonmilitary faction of the boy scouts, in the political spectrum you might called them the conservative antiauthoritarians)

The next three are examples from the left-wing folksong revival in the 1960s. They are more or less interchangeable with a big overlap in songs. One of them would be enough for a collector:

H. & O. Kröher, Das sind unsere Lieder (These are our songs), Edition Büchergilde, no date
notes: 218 songs with tunes and short annotations
comment: more international in the choice of songs than the other two; a rare find in it is a German version of Whiskey in the jar

T. Friz & E. Schmeckenbecher, Es wollt' ein Bauer früh aufstehn (a farmer wanted to stand up early), Pläne Verlag, 1978
notes: 222 songs with tunes and short annotations
comment: more old German songs than the other two

A. Stern, Lieder gegen den Tritt (songs against the marching step), Politische Lieder aus fünf Jahrhunderten (Political songs from five centuries), Asso Verlag, undated.
notes: more than 300 songs with tunes and short annotations
comment: more political songs than the other two)

H.W.Schmidt, Uns geht die Sonne nicht unter, Lieder der Hitler Jugend (The sun doesn't go down for us, songs of the Hitler youth), 1934, out of print in Germany, no reprints allowed, only available outside of Germany second hand at those places where you get Nazi symbols and all that crap
notes: about 150 songs with tunes and without any comment, attentiononly available in Fraktur print (see Zupfgeigenhansl)
comment: I have long considered not mentioning it here but I have decided to include it for its historical value and to add an antidote (next entry); many of the songs are common German folksongs, only about 20% of them are explicit Nazi songs

no editor, Das Lagerliederbuch, Lieder gesungen, gesammelt und geschrieben im Konzentrationslager Sachsenhausen, 1942 (songs sung, collected, and written in Sachsenhausen concentration camp), Pläne Verlag, 1980.
notes: about 130 songs without tunes and annotations, attention in reprinted handwriting, not always easy to read
comment: this is a reprint of a handwritten illegal booklet existing in Sachsenhausen concentration camp in which the inmates collected their songs, old and new. The famous anti-Nazi songs (e.g., peatbog soldiers/Moorsoldaten) are in there as well as common German folksongs. Some of the songs are even the same songs as found in the Hitler youth songbook of their wardens.

K. Schilling & H. König, Der Turm (the tower), Voggenreiter Verlag, 1952ff (new editions continuously altered)
notes: more than 500 songs with tunes and chords, but not annotated; attentionmy fairly recent edition is still in Fraktur print (see Zupfgeigenhansl), I don't know if the very conservative boy scouts leadership considers compromising with modern times regarding the print
comment: the songbook of the boy scouts, songs old, new and international

H. Buhmann & H.P. Haeseler, Das kleine dicke Liederbuch (little thick songbook), 3rd edition 1983, own printing, out of print now according to Amazon, will be reprinted soon
notes: more than 300 songs with tunes and chords, short annotations
comment: songs that are sung in Germany today, most still in German, from old folksongs to very new songs from the hit parades, the German equivalent to 'Rise up singing'. If you want to buy only one book to be able to sing with Germans when meeting them, you should buy this book.