outside the USSR (and maybe northern France + the Low Countries in 1944) there was no way to tangibly measure the battlefield effect that they did have.
There was also in some other places.
Yugoslavian partisans liberated their country with only little help from the Red Army (and of course with help of vast equipment supplies from the Allies). In Poland partisans are also credited with liberating some towns & small cities - either alone, or in cooperation with the Red Army or with Soviet partisans.
Yugoslavia had the largest armed resistance movement of WW2. Here is a good website (vojska.net):
Here a very detailed chronology of WW2 in the Balkans:
http://www.vojska.net/eng/world-war-2/battles-and-operations/
By the end of WW2 Tito's partisans were so well equipped that they were practically a regular army.
Combats against regular Axis forces in Yugoslavia lasted until 15-16.05.1945 and against Axis Croatians (NDH) until 25.05.1945.
In April and May 1945 Yugoslavian partisans for example destroyed SS Division "Prinz Eugen" on their own.
I don't think any other partisans of WW2 can be credited with destroying a German division in battle.
According to the Soviet historiography, Axis losses totaled more than 53,000 soldiers.
Which is almost certainly exaggerated (as all figures concerning enemy losses usually are).
When it comes to the Balkans - here the Germans lost in combat vs. partisans (KIA, MIA, WIA) - according to their own data, not enemy data - 93,000 soldiers during the period 01.01.1942 - 20.04.1945, but we can suspect that the German casualty reports from 1945 (34,500 reported combat losses) are underestimated, as they had problems with accurate reporting at that time, due to catastrophic defeats. So losses for 1945 were most probably greater.
And as can be seen, losses were reported only until 20 April 1945 - so all losses from May (including destruction of "Prinz Eugen") are not here yet.
In case of Yugoslavian resistance, until August 1944 they were partisans, while since September 1944 they acted more like regular army.
Since November 1944 Yugoslavian resistance movement included - for example - one armoured brigade. Later 2nd one was fielded.
Yugoslavian partisans also had a casualty reporting system - they reported 622,000 losses (KIA, MIA, WIA) for 1942 - 1945.
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Wikipedia about "Prinz Eugen" is a bit less dramatic than I've read elsewhere - it writes not about destruction, but surrender:
http://en.wikipedia.org/wiki/7th_SS_Volunteer_Mountain_Division_Prinz_Eugen#1945
In January 1945, the division was again in action against the Yugoslav army at Otok and Vukovar. In February it took part in Operation Wehrwolf against Yugoslav bridgehead in the Virovitica area.
The retreat from Bosnia continued and Prinz Eugen retreated through the NDH in April 1945. On 10 May, the division retreated towards Celje in Slovenia where it surrendered on 11May to Yugoslav forces.
But they forgot to mention, that after capitulation most of SS prisoners were killed or died in Yugoslav captivity.
So "Prinz Eugen" still had to suffer very high losses in May 1945, even if actual combat losses were small.