During the war, some of German military production was located in the Protectorate of Bohemia and Moravia. Seeing that the production capabilities and several pieces of equipment were already there, Czechoslovakia (basically rebuilding its army from the ground up after the war) proceeded to use or develop its own versions of German equipment. Avia S-99 was pretty much just a Czechoslovak-assembled Messerschmitt Bf 109 G or K.
Avia S-199 was the same model but with an engine and propeller originally used on the Heinkel He 111 bomber (due to shortages), giving the aircraft some questionable handling. This model was also exported to Israel (along with thousands of weapons and massive amounts of ammunition supplied by Czechoslovakia, including Czechoslovak-produced Karabiner 98k rifles) and saw action in the 1948 Arab–Israeli War.
Czechoslovakia also had access to parts and design documents to the Messerschmitt Me 262 jet fighter. 12 were produced under the name Avia S-92, of which 3 were jet trainers.
Another vehicle used by the Czechoslovak Army was the Sd.Kfz. 251 halftrack, which was later (entering service in 1959) developed into the OT-810 which had an air-cooled engine, but was overall badly designed.
Erma Mp 38/40 Several armies used it
Sturmgeschütz III Ausf G, mostly
Need I have to mention the Mauser K98? Several countries
The ubiquitous Flak 36/37 88mm
StG 44 (MP 44?)
These are the ones that come from the top of my head. Many more are surely out there.
Other people have already given more broad answers that better answer the actual question, but I just wanted to point out that StG-44s are being used in the Syrian Civil War. StG-44s and MP-40s were also used by the Viet Minh and the Viet Cong in the Vietnam War.
So aside from their official usage by countries, German weapons can still be used any group if they have access to them just like any other weapon.
