It is a bit more complicated, though: German, as any other language, needed a word for that, and it needed it badly, but it did not have one until the mid-'90s, where it took it probably from the Spanish expression vergüenza ajena, which is a literal translation for fremdschämen. Here you have the dictionary entry for fremdschämen where they say they did not include this word until 2009.
The fact that people my age must have been witness to the introduction into the German language of this term combined with my observation that none of them remember this process, all swearing that this word has always been German, shows that the word was really badly needed. The adoption of this neologism has been nothing short of enthusiastic.
My theory is that the word was immediately coined when Big Brother was aired for the first time (around 2000). It just had to be.
Or even “It’s not just yourself you’re embarrassing, you know”
“Cringe” didn’t always mean “wince,” either. If you look in older dictionaries, the only definition will be something like “bow one’s head in a servile manner.” (Tim Rice used the word that way in “Joseph and the Amazing Technicolor Dreamcoat”: “Grovel, grovel, cringe bow stoop fall.”)
Indeed, the origins of the word carry the connotation of bowing in servility or fear.
Still, the idea of “bowing” one’s head out of shame is not much of an expansion, and the application to bowing one’s head out of vicarious shame fills a real need, unless we would like to borrow the German neologism instead?
There are words in German and Spanish, which I learned in this thread.
ETA: I see they’ve already been mentioned a couple of times but I provided links. 
I’d say “that speech was cringeworthy “
Cringeworthy- causing feelings of acute embarrassment or awkwardness . So embarrassing or awkward it causes one to cringe
OK, Boomer.
–Gen X-er 
Cringeworthy really means that the person giving the speech should be embarrassed. Cringe would imply that we were all cringing for the speaker. At least in my internal dictionary.
Well I’m a gen X but British origin, if that makes a difference, I wasn’t correcting you just saying what I would say . For me cringeworthy in the context of the speech h example is more or less “I’d be embarrassed if I was in their shoes “
Borat and the Office are cringeworthy to watch.
I think so too. It can be internal or external as well.
The feeling is one of the 175 meanings Southern women use the term “Bless her heart” to cover.
I still say cringe more narrow than embarrass. There needs to be some willfull action or inexcusable failure to anticipate leading to the embarrassment.
I heard on the radio this morning that DePaul University Chicago men’s basketball had a 3-28 season. Embarrassing but not cringe.
BBC Dad, embarrassing (and tearjerkingly funny) but no cringe.
Here they are today, 7 years later:
https://www.reddit.com/r/pics/comments/1bb5ndi/family_of_robert_kelly_a_bbc_dad_whose_kids/
My gf’s high school girl’s basketball team didn’t have enough schools in their division to play a full schedule, so they played one game against a bigger school. They were shut out. In basketball. Cringe?
No and, if they were playing an opponent well beyond their division/standing/weight class, arguably not even embarrassing.
Heh, once they were down 20-0, they pretty much gave up and were laughing. Unfortunately, this was back in the day before video recording was common.
I caught the last few minutes of the Bulls Mavs game this Monday where Chicago lost 127-92. THAT is embarrassing.
I tend to think that the OP’s requirement is not really met by any of the English words or expressions. Cringe has become used, in addition to its original meaning to cover the idea, but it isn’t great.
The experience is something quite interesting. We have an entire function of our brains devoted to modelling what we perceive in others. Lots of good reasons for having it, and lots of philosophical questions about it.
Being embarrassed for someone one would imagine is rooted in exactly this function. Our brains are engaging with the other person and the modelling function is trying to follow them. When they start doing something that the watcher regards as embarrassing, this somehow feeds into the watcher’s own emotional response.
Lots of suppositions here. But there is lots of work on the ideas.
Cringing is of course the physical manifestation of the embarrassment. The trouble with the word is that is also applicable to someone who is properly embarrassed themselves.
But Cringe Comedy is a perfect description of the type of situation comedy that lays on this.
An interesting question is whether one feels the emotion when the character being watched is thoroughly unlikeable. Basil Fawlty is not exactly someone one would enjoy inviting for dinner. But there is a certain pathos to the character as well. So perhaps that helps.
There seem to be other emotions than embarrassment. This seems especially so with comedy where one character is eternally put upon, or is written as an all time loser.
Decades ago there was a comedy series on TV here. There was a running story we got a bit of each week featuring an all time nice guy loser who shared a house with a ridiculously beautiful girl who had a deadshit boyfriend that she stayed with because of the sex. There was one moment where nice guy was just about to get lucky with girl. Then of course there is a twist and it doesn’t happen. You could hear the chorus of the studio audience collectively going “oh no”. I think they wanted to hunt down the script writers for being so mean.
Douche chills