I found a museum quality sherman in Iraq when I was there the last time. It was up on the northern end of Taji, there was also a Walker Bulldog. Those I can understand, US aid or the Brits left them. Both of them had US markings on them though (could have been put on by the capturing unit though). The Sherman still had the bow MG in it! I also scored a PPsH from an Iraqi when I was there, but, I had to turn that in.
I saw some clips of T-34s running around Africa from just a few years ago, I think it was from the Congo, or one of the central African countries.
Angola was still using T-34/85s in Africa.
T-34-85s were used extensively throughout the Korean War, Vietnam, several Central African Confilcts, and during the Balkan wars. One of the Osprey modeling manuals has a model project where soemone took a T-34-85 and put graffiti all over it.
The Chilean arsenal still has a number of M-51s it purchased from Isreal.
Several Central and South American countires still use M8 and M-20 armored cars, or variants based on those chassis.
Some the coolest uses of postwar equipment I’ve seen were the Sherman “construction vehicles” from a couple of photos; the civilian DUKWs already mentioned; and the conversion of a Leopard I to a firefighting vehicle.
Portuguese colonial infantry (“cacadores indigena” I think) used Mauser 98k rifles in Angola into the 1960s.
There was still a Ju 52 doing weekly sight seeing flights in Johannesburg, South Africa, at least until about 10 years ago. Don’t know if it’s still flying.
(Speaking of southern Africa, I saw a picture from the 1970s of a British Universal Carrier being used in the guerilla war in Rhodesia.)
My personal favorite post-war use of Wehrmacht equipment: Polish farmers were reportedly using Panther road wheels on their horse carts into the 1980s. 
The Syrians also had Stug III’s, a few Hummels, and Jagdpanzer IV’s. The Stug III’s saw combat alongside the Pz IV’s against the Israeli’s. I have pictures on my website of one of the Pz IV’s in a museum here in the US.
Chris “toadman” Hughes
http://www.toadmanstankpictures.com