2 years ago when I went to Germany on leave with my aunt, we rented a car at their version of Enterprise in Heidelberg. All we had to do was show our stateside DLs (And mine was even expired by 15 days but still good with the mil ID, heh). Didn't have any issues. We drove to France and back (Strasbourg, to catch the Prologue of the Tour de France).
Like M2 said, the big asspain was trying to get my Aunt on base. First the German gate guards didn't want to let me on since my CAC wasn't in their system, and then they didn't want to give me escort privileges. Finally got documentation from the Provost Marshall that I was allowed, by virtue of being AD mil, to escort up to 4 individuals on base, and then it wasn't a problem. It's funny b/c we were there for HER brat reunion (grandfather was stationed at Heidelberg), and she was on an EAL at the HQ, but not the housing areas or the PX.