In A New Hope, he translates R2D2 while they're on the Death Star and R2's getting information from the computers.
Early in Return of the Jedi, while he's working for Jabba.
Later in that film he translates Ewok into Basic, AND provides protocol information about why his friends are going to be killed and cooked.
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If I remember correctly he does some translation in the beginning of A New Hope .
He translates some of R2D2's talks especially while Jawas are selling the droids to them.
Also he does some translations between Ewoks and others.
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Remember we never see (except possibly during the closing scenes of RotJ)
C3PO in a setting where his function as a protocol droid would be beneficial.
His job is as a court functionary, not a fugitive smuggler or warrior in a rebel band.
As to everyone speaking common, Jabba the Hut didn't.
Nor did several of the people in Mos Eisley so not everyone in the SW universe speaks the same language.
The fact that everyone (or almost) the main characters come into contact with does may be either a fluke or designed that way to make the movies easier on the audience.
A conversation that takes over twice as long as it should because every sentence has to go through a translator doesn't make for very good cinema after all, so I call artistic license here.
The fact that Leia had a protocol/translator droid with her on her diplomatic mission indicates to me that she did expect to need those services in some capacity.
It just never made the cut.
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This answer addresses both the original question (e.g. whether C3PO ever did his job) as well as clarifies the discussion in the comments on whether his job was "protocol" as in communications protocol or "protocol" as in diplomatic protocol (e.g. etiquette).
The short answer to the latter is that it was the latter (etiquette) but as part of that purpose he was definitely designed as a specialist in communications protocol.
He was the protocol (in diplomatic sense)
droid, both by design and sometimes (relatively rarely) by function.
This was noted in post-ROTJ books, as well as the following source quoted in Wikipedia: in 1977, Lucas provided a guide for early Expanded Universe creators, in which Threepio's origin on Affa was established, and also the fact that he was "totally reassembled by a young boy working for a junk dealer" before joining the Alderaanian diplomatic corps "several years" later .
Also, from starwars.com Protocol droids are vital in smoothing differences encountered by the many farflung cultures interacting on a regular basis throughout the galaxy.
Programmed in etiquette and equipped with formidable language skills, protocol droids assist diplomats and politicians and also serve as administrative aides and companions for high-ranking officials.
he actually fulfilled that diplomatic function (as opposed to simple translator) a couple of times when Leia was serving as official of New Republic.
I don't have specific book quotes but Wiki C3PO article lists a couple of obviously diplomatic assignments.
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Yes.
In the original trilogy, he does his job in each of the three movies.
Episode IV
Translating R2D2's beeping-whistle language for Luke.
Specifically, translating R2's warning about the approaching life forms (Sand People) on Tattooine.
And most importantly, telling Luke that R2 has located Princess Leia aboard the Death Star.
Episode V Speaking with the Millenium Falcon to help diagnose its problemswhile in the asteroid field.
Translating the language of love between Han and Leia, and interceding at the most inappropriate time for the two of them.
Episode VI
This is where C3P0 really gets to shine.
Translating for Jabba the Hutt, which while not exactly heroic,
IShis job as a translator.
Translating the Ewok language for therebel strike team.
Most importantly, translating the strike teamfor the Ewoks, and convincing them that he is a Golden God of greatpower and anger.
I can't recall him doing any sort of translating in the prequel trilogy though, not even for R2.
Though presumably he may have, at some point, acted as translator for Owen Larrs.
And at the beginning of Episode 3, he's clearly working for Padme in some regard, though we never see any of it on-screen.
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C-3PO is a protocol droid that is fluent in over six million forms of communication, but it seems like everyone in the galaxy can understand every other language.  Has C-3PO ever had to translate?  I do recall him translating R2's beeps at one point, but I'm not positive.
Does C-3PO ever do his job?
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He does translate in all of the movies in the original trilogy. For example, In A New Hope, he translates R2D2 while they are on the Death Star and R2-D2 is getting information from the computers.  He also translates for R2D2 when Jawas are selling the droids to them. He later translates Ewok into Basic, and provides protocol information about why his friends are going to be killed and cooked. C-3PO does his job in all movies of the original trilogy. He translates Ewok into Basic and translates for R2D2.
C-3PO does his job in all movies of the original trilogy. He translates Ewok into Basic and translates for R2D2.