Of all four that I've watched already, I strongly recommend watching 127 hours. I really believe James Franco could have won the Best Actor award if not for Colin Firth -- in fact, I really believe the movie could have won Best Picture, again, if not for The King's Speech. (And this is exactly why I looked for the the latter because I have not watched it yet.)

127 Hours is a 2010 biographical adventure film produced, co-written and directed by Danny Boyle. The film stars James Franco as mountain climber Aron Ralston, who became trapped by a boulder in Robbers Roost, Utah, for more than five days in early 2003 before amputating his arm with a dull knife. - Wikipedia.
Let me just clarify that: He was trapped in that very same location because the boulder landed on his arm. He cannot escape and even if he wanted to cut his arms as early as in his first day, he wasn't able to do that because his knife was very, very dull. His water is just in a 1-liter or so container, he has limited food, of course, and, well, noone is searching for him because he didn't tell anyone what he plans to do and where he is going. He only succeeded in amputating his arm on his 5th day. (One can only wish he had SSDI benefits when he did that.) So, the story is about the 5 days he was in that location.
I'll be watching The King's Speech later. :-)