12 Angry Men (1957)

Directed by Sidney Lumet

One can definitely see why it's considered a classic. A little ridiculous that it's ranked as the number 5 best movie on IMDB though. But it is a good movie. It's a call for non-conformism that probably hit a bit harder in 1957 than it does today. It feels a bit "stagey". Doesn't use the film medium very well. It was Sidney Lumet's first movie though, so I have say in that respect it is very good.

The Wrong Man (1956)

Directed by Alfred Hitchcock

A different sort of picture for Hitchcock.  Instead of his usual suspense thriller this is what you might call a docu-drama.  An attempt to realistically paint a picture of events as they really happened.  A fascinating look at how an innocent man can get caught up in the criminal justice system.