Of course you can not do any such list without having the quintessential Great Escape from 1963. It is the incredible true story of the mass escape of 76 Allied POWs from Stalag Luft III in March of 1944. This has a huge all-star cast, featuring many of the heavy hitters of the day--- Steve McQueen, James Garner, Charles Bronson, and James Coburn (incidentially McQueen, Bronson and Coburn appeared together in the Magnificent Seven, one of my favorite westerns). This movie appears fairly regularly on television (actually they both do), but if you missed it, or just want to revisit it, now is the time. It is a great story.
Rescue Dawn from 2006. This film tells the real-life story of U.S. fighter pilot Dieter Dengler, a German-American shot down and captured in Laos during the Vietnam War. He was the only known POW to escape from a Laos prison. It features Christian Bale (Batman Begins) as Dengler. Bale looks rail thin here, but not as bad as in The Machinist, a role for which he lost an astonishing 63 pounds. Bale, an actor known for fully embracing his characters (as witnessed by what he regularly puts his body through) does in fact, eat those maggots.
Papillon from 1973 again with Steve McQueen and Dustin Hoffman as inmates of the notorious Devil's Island in French Guiana circa 1930's. This movie was incredibly popular at the time of its release, and being a period piece actually stands up well. Ocassionally a little campy, it still tells a remarkable tale of hardship, endurance and ultimate triumph.
The Killing Fields--- Covering the U.S. pullout from Vietnam in 1975, this is the story of two men---a New York Times correspondent and his Cambodian friend and translator Dith Pran. The reporter coerces his friend to remain behind in order to keep filing news reports. As Saigon falls the correspondent is released, but Pran is captured by the dreaded Khmer Rouge. The rest of the film details Pran's harrowing experiences at the hands of the Khmer Rouge, and his attempt to escape. This is an excellent movie but has very graphic scenes of violence.
These first four are all movies based on real life events. For some good fictional 'triumph over adversity' stories, try Cast Away with Tom Hanks from 2000---the plane crash is amazing, as is the self dentistry!
Or how about the popular television series Prison Break from 2005.
Want to get your head bent? Try any or all of the 17 near psychedelic episodes of The Prisoner from 1967. Not into the 60's groove? How about Alexander Dumas' Count of Monte Cristo--- we have two versions---French with Gerard Depardieu and the quite stylish 2003 with Guy Pearce and Jim Caviezel---who is currently starring on tv in a remake of----The Prisoner.