Actually almost all Waffen-SS divisions had their own cufftitles featuring the name of their regiment (Standarte) or division.
Some elite units in the German Heer were autorised to wear cufftitles too (GroBdeutschland p.e., or the Branderberg regiment/division).
Next to that a relatively large amount of Luftwaffe air and groundunits were issued Armelstreifen also ("General Goring" being a prime example, with some Jagdgeschwader, Kampfgeschwader en Fallschirmjaeger units being others).
And that's not even counting the Kriegsberichter (war correspondents), the Kragenpatten being worn by some Waffen-SS units, the regimental numbers and cyphers being mentioned above, the U-Boot insignia which were often worn by their crews and ofcourse the unofficial unit insignia made in the field.
But to answer your question: German units generally did not wear unit insignia in the way US units did. Some (most?) German divisions did have an unique divisional emblem, but almost none of these were ever issued as a patch/insignia.