I can't tell you anything theoretical about german poetry, but I can give you a few famous examples:
Andreas Gryphius: Tränen des Vaterlandes
This poem was written during the time of the Thirty Years' War. Up to today it is considered as one of the most touching german poems. This youtoube-reading hits the mood pretty well, but sadly differs from the original a few times. Especially at the end it should be "dass auch der Seelen Schatz", still worth to listen.
http://www.youtube.com/watch?v=5Rje9d8zflw
It begins at 2:40
Goethe: Prometheus
Schiller: Nänie
Hölderlin: Hälfte des Lebens
Goethe, Schiller and Hölderlin; those three are propably the main reason for the "land of poets".
http://www.youtube.com/watch?v=ocvjp2aQb_g
http://www.mediaculture-online.de/fileadmin/mp3s/schiller_naenie.mp3
http://www.youtube.com/watch?v=qzR0OH-2sQ4&feature=related
Heinrich Heine: Nachtgedanken
Heinrich Heine: Lore Ley
At least the first few lines of Nachtgedanken are known by everyone. Lore Ley was made into a song later and got really famous. I think Adorno once said that it got so popular that even the nazis could not get rid of it, even though they tried to ban all of Heines work. At the end they gave up, but changed the authors name into unknown. You will hear this anecdote every now and then.
http://www.youtube.com/watch?v=vP0KlFvRtjQ
http://www.youtube.com/watch?v=4sK-AZko76Q
Rilke: Der Panther
I think it's Rilkes most famous poem. I don't like everything from him, but this indeed is beautiful.
http://www.youtube.com/watch?v=xsAvANPIPkw