Germans made extensive use of captured equipment. An example:
21st Panzer division when reformed in July 1943 had a tank regiment (100th Panzer Regiment) that was made up from various independant companies that were equipped with French Hotchkiss and Somua tanks. On May 20, 1944 the unit was re-equipped with PzKpfw IVs in place of the French tanks.
There were some Luftwaffe units that used captured aircraft, most obvious being KG 200 and I believe LG 1 in the beginning.
On the Allies side, 325the FG in North Africa had both a Bf 109 and Fw 190 although I don't think they were used operationally.