Hi Bob,
yes, theres one in Stuttgart, about 10 mins from where I'm based and a few others dotted around.
Just had a look at the LDS site. There is one in Berlin:
Berlin Germany
Klingelhöfer Straße 24
Berlin, Berlin, Berlin, Germany
Phone: 49-30-25794336
Hours: Wed, Thurs 14:00-20:00; F 16:00-20:00; Sat 9:00-13:00
Otherwise, on the LDS homepage, go to "Library", then "family history centers" and choose the country/city you want.
Unfortunately, there are none where I am at the moment

D