I have heard a lot of storys of aillide POWs excaping but I have never heard any storys of aillide POWs excaping.
If you are implicitly asking about successful escapes, speaking for the Western Allies (US/UK-Commonwealth), No. Escape attempts from the American, British, and Commonwealth run POW camps were few and far between, and almost universally unsuccessful, and the very few contrary examples were very small attempts. A few large groups did try, but never made it. Off hand I know there was a German who escaped from a Canadian camp before the US entered the war, and so was able to get to the neutral country and then back to Germany, and there was a German, Reinhold Pabel, who escaped an American camp, and while he didn't get out of the country, managed to live under an assumed identity in Chicago for nearly a decade. I don't believe there were any successful attempts from camps in the United Kingdom.
The simple fact is that there was little incentive to try, despite the fact that security conditions were often considerably more lax in Allied run camps than German run ones. The isolation of the camps from any chance of real success was a serious deterrent, and even though attempts were made, many (when caught) would reflect that it was more a matter of going through the motions. While an escapee in Germany could count on the possibility of help within a few hundred miles if only they could make it to one of the occupied nations, an escapee in the United States had no chance of real help, and even in the UK, the channel was a near insurmountable obstacle of course.
Reflecting on his encounters with several escapees in Illinois, a local sheriff noted:
[T]hey made us feel kind of sorry for them, these German escapees. We would find them there, in the streets, without a word of English, in Bloomington, in Peoria, in Galesburg; or else in the woods, completely lost like strayed sheep. Yes, I tell you, it was rather pitiful. Besides, local people weren't afraid of them. When they met up with one, they called us; we came, put a hand on their shoulder, and gently brought them back to camp.
Would recommend 'Nazi Prisoners of War in America', by Arnold Krammer
There was the "Cowra Breakout" which involved a mass breakout of Japanese POWs from Camp B of No 12 Prisoner of War Compound near the town of Cowra in New South Wales (Australia) on 05 August 1944. The purpose of the breakout wasn't clear as the prisoners had no chance or apparent expectation of getting from Australia to either a neutral country or home and the escape was initiated by suicidal attacks on armed guards, including overrunning a machine gun point armed only with makeshift clubs and knives.
Of the 1,104 Japanese prisoners in the camp, 234 were killed, 108 wounded and 334 escaped into the surrounding countryside to be rounded up over the next nine days. None are known to have stayed at large over an extended time or to have escaped Australia.
You can access detailed official documents relating to the breakout at National Archives of Australia