I haven't seen Hogan's Heroes so I can't comment on exactly how accurate it is, but yes, allied prisoners of war were engaged in espionage, a great many escape attempts, and various other activities designed to make the lives of their captors difficult. This was greatly aided by an organisation called MI9, and their US counterparts in MIS-X.

MI9 was set up by the British Intelligence Services to oversee matters relating to prisoners of war, both those in enemy hands, and enemy prisoners held by Britain (although the enemy prisoners section would be split off into MI19 in 1942). MI9's mission was to aid British soldiers in escaping from captivity and returning to Britain in any way possible. There were multiple motives for this. Firstly, they could return to the manpower pool - while simple infantry soldiers were in good supply, there was a shortage of trained pilots and aircrew. Secondly, any escaping soldier would tie up enormous amounts of manpower searching for them, thus disrupting enemy activities. Finally, returning soldiers were valuable sources of intelligence. If they had escaped from a PoW camp in Germany then they could tell the intelligence services all kinds of valuable information that they picked up.

MI9 took a number of steps to prepare soldiers for possible captivity. They gave lectures and showed films about tactics the Germans might use to get soldiers to betray information, and used lessons learned from escapees in the First World War.

In addition, MI9 identified a number of officers and NCOs in roles which might lead to them being captured, and trained them in the use of coded letters, allowing them to communicate directly with prisoners in camps. While the post system between POW camps and Britain was very slow, with letters taking months to arrive, it nonetheless allowed POWs to pass on intelligence, and request that various escape supplies be smuggled to them in food and comfort parcels distributed by fictional British organisations.

Escape from a POW camp was relatively difficult, returning home was even more so. To aid POWs in their efforts to escape, MI9 distributed large numbers of cleverly disguised escape aids. The top button of RAF uniforms could be separated into a tiny compass, razor blades in shaving kits were magnetised with the manufacturers logo indicating north and compasses were hidden in everything from smoking pipes to pencils. Grey blankets sent into POW camps were printed with the designs for German uniforms and clothing which would only be revealed when dipped in a certain combination of chemicals, these too had to be smuggled into camps. Board games sent to entertain bored soldiers could contain all kinds of tools - monopoly sets could contain a wealth of secret devices. There were even saw blades hidden in shoelaces.

An essential item for an escaping soldier was a map, MI9 printed over a million of them during the war. Traditional paper maps were too difficult to hide and made noise which could give an escaper away, so MI9 printed maps on silk, tissue paper and later nylon. The maps covered Europe in some small detail, and were often inset with much smaller scale maps. For example, some maps had detailed depictions of the port of Danzig, where many escapers managed to smuggle themselves onto Swedish ships.

Actually getting items into the camps was easier said than done. The official Red Cross aid parcels were strictly off limits so MI9 instead established a number of fictional societies whose parcels were filled with escape supplies. While supplies often were found by the Germans, parcels could often be rescued by POWs put to work in the post room. Camp Guards were often poorly motivated and trained, and could be easily bribed to look the other way. Some prisoners even managed to obtain firearms from friendly guards.

While many prisoners were content to sit out the war, a large number were determined to escape or to cause as much nuisance as possible. Even an unsuccessful escape tied up huge amounts of German manpower. It is estimated that when fourty officers escaped from Oflag VII-B in Bavaria, they tied up 40,000 soldiers, police and Hitler Youth. The largest escape from a camp, the so-called Great Escape of 76 officers from Stalag Luft III, tied up an even larger amount of men.

For more on MI9, see Helen Fry's MI9, which is a more modern version, or Foot and Langley's MI9, which, although dated, was written by a former MI9 Officer and a former SAS soldier, both of whom actually managed to escape from captivity in WW2.