In Spanish, vergüenza ajena describes the embarrassment you feel on someone's behalf. Say, a person stands up and sings horribly, or a man makes a fool of himself trying to pick up a woman. It's an empathetic feeling you have when watching them.
When it was first described to me, I had no idea how to translate it, much less what it was. I simply said, "We don't feel that." But since then, I've noticed that the trademark performances of Ben Stiller and Ricky Gervais tend to generate that feeling, specifically when they begin to say something ridiculous, try to find a way out, and then ultimately get trapped in a long awkward silence. It's that kind of feeling.
Curiously, since having a phrase to describe this (albeit in Spanish), I've become much more aware of it. It's like the feeling has suddenly come into existence.
Best Answer
According to Wikipedia the phrase you’re looking for is, surprise, surprise: vicarious shame:
It is quite an apt phrase too. Merriam-Webster defines vicarious as:
The phrase appears to have been around for some time. You can find a few instances in Google books. For instance, Silvan S. Tomkins, Affect Imagery Consciousness, Volume III, 1963, p. 225: