Absolutely everything I know about WW2 prisoners of war comes from reading The Great Escape. It references a handful of leisure activities--lecture attendance, theater, gardening, art, endless walking. But the only sport-type thing I can possibly think of is the vault set up for "gymnastics drills" (also known as disguising tunnel construction). Surely there was some form of organized athletic competition? Or was that prohibited by the Germans on some grounds or other?
I'd be interested in the experience of Allied or Axis POWs, with the understanding that the answer is going to vary tremendously depending on country of origin, place of internment, etc.
P.R Reid talks a bit about sport in 'The Colditz Story' (1952).
Most of the exercise at Colditz castle (Oflag IV-C) was in a fairly small courtyard, so there was a tendency towards sports that didn't take up much space. There were some foils for a while, so a number of people took up fencing. Boxing and a kind of volleyball were also popular.
There was another game they played which he's got a fairly long section on which I will mostly copy out:
'There was one game which deserves special mention It was invented by the British and belonged to that category of local school game devised in almost every public school of England [this was an officers' camp of course]... The Colditz variety, which we called 'stoolball,' was played, of course, in the granite cobbled courtyard. It was the roughest game I have ever played, putting games like rugby football in the shade. The rules were simple. Two sides, consisting of any number of players and often as many as thirty a side, fought for possession of the football by any means. A player having the ball could run with it but could not hold it indefinitely; he had to bounce it occasionally while on the move. when tackled, he could do whatever he liked with it. A 'goalie' at each end of the yard sat on a stool—hence the name—and a goal was scored by touching the opponent's stool with the ball. Goal defence was by any means, including strangulation of the ball-holder, if necessary. There was a half-time when everybody was too tired to continue. There was no referee and there were, of course, no touchlines.'
Despite how dangerous this sounds, the author says that he never saw anyone seriously hurt. He speculates that the game was a sort of manifestation of their desire to be free: 'The surrounding walls were no longer a prison, but the confines of the game we played, and there were no constraining rules to curtail our freedom of action. I always felt much better after a game. Followed by a cold bath it put me on top of the world.'
Later, when they were allowed a few hours exercise in a larger wooded area every week, a kind of football was played. These prisoners were getting Red Cross parcels, (or in the case of the French and Poles, packages directly from home) so, while they were certainly hungry, they still had enough energy to do stuff like this sometimes, whereas the Russians were mostly very near starving.
The Imperial War Museum have a number of photographs of British prisoners playing sports, including boxing at [Stalag Luft III] (http://www.iwm.org.uk/collections/item/object/205087217), cricket at Stalag VIIIB and rugby at [Stalag VIIB] (http://www.iwm.org.uk/collections/item/object/205234558). There's a large collection from [Stalag XXID] (http://www.iwm.org.uk/collections/listing/object-205009314), including many shots of rugby, boxing and (association) football.
The American National Red Cross published a Prisoners of War Bulletin, several issues of which can be found at [archive.org] (https://archive.org/search.php?query=%22prisoners+of+war+bulletin%22&sort=date). The November 1944 issue says that "a six hole golf course was laid on at Stalag Luft III (Center Compound)", including traps, bunkers and greens, playing equipment consisting of one set of clubs and four balls, more being made from salvaged rubber and leather, but notes that German authorities had recently suspended intercompound sports (Stalag Luft III consisted of a number of separate compounds, three American, two British).
The March 1945 issue has a small piece, "Sports at Luft III", which says that football (presumably American) was the main sports activity at Stalag Luft III in October and November, and the men were waiting for frost to begin the ice hockey season. There are also photographs from Oflag 64 of prisoners playing baseball, and pitching horseshoes.
Most comprehensively, there's an article by Pamela Cohen in Sporting Traditions, the journal of the Australian Society for Sports History: [Behind Barbed Wire: Sport and Australian Prisoners of War] (http://library.la84.org/SportsLibrary/SportingTraditions/2006/st2301/st2301h.pdf). According to that, "Australians in Stalag 383" (500 out of 5,000-7,000 prisoners) "participated in Australian Rules football, cricket, rugby league, rugby union, soccer, basketball, baseball, boxing, wrestling, hockey, softball, swimming events, volleyball, water polo, golf, and a variety of athletics events."