At the start of A New Hope, when the corvette is being attacked, C3PO says something to the effect of:
There'll be no escape for the princess this time.
But when Luke stumbles onto Leia's message in R2D2, C3PO seems to not know who the figure in the message is:
I'm afraid I'm not quite sure, sir. I think she was a passenger on our last voyage. A person of some importance, sir - I believe.
Is C3PO feigning ignorance to protect her, or does he really not recognize her?
George Lucas spoke to this issue in an interview in July 1977, transcribed in The Making of Star Wars: The Definitive Story Behind the Original Film
In a series of three radio interviews, Lucas pretended to speak as three of the characters from Star Wars film; Leia, Han and C3P0. When asked a question about C3P0's knowledge of the Princess he replied;
"There are literally hundreds of Ambassadors, to many systems, including several ambassadors from Alderaan. We would take ambassadors and important government people from Alderaan to all over. Mainly I'm an interpreter robot. If we found alien life-forms or if we were on a planet where they did not speak the Universal Galactic Language, I would have to translate. So I wasn't really in on what was going on. I was programmed to mention having no knowledge of the Princess - that she was aboard the ship. That's why I always seemed ignorant when she was brought up. I knew who she was, but I was programmed not to say who she was"
I'll have to go watch it again to confirm.. But remember; C3P0 had his memory wiped at the end of the prequel trilogy (so he would have no background knowledge of her) and, although we see R2D2 with Leia, I don't know that C3P0 was formally introduced to her.
His comment about her not escaping indicated that he knew she was on-board, but if he had not 'met' her, he may have guessed that the image was her, but having no formal knowledge, chose not to state so.
Update I just watched it; and where R2 is getting the message from Leia, C3P0 is wandering around asking "R2D2, where are you?" before spotting him down the hall, with a somewhat cloaked Leia. He doesn't ask anything about what the Princess wants or anything, so I would surmise he didn't know who R2 was interacting with. He also has no clue about what 'Secret Mission' R2 is on (before boarding the pod, and later, on Tatooine, he asks what mission R2 is talking about)
When Luke asks him later about their background you get this quote:
He says he's the property of Obi-Wan Kenobi, a resident of these parts. And it's a private message for him. Quite frankly, sir I don't know what he's talking about. Our last master was Captain Antilles, but with what we've been through, this little R2 unit has become a bit eccentric.
Give that Threepio thinks of himself as belonging to Antilles, it's not unreasonable to assume he may not have met the princess directly.
My guess, and the only way I've thought of so far to reconcile these two, is this:
C3PO knew the Princess was on the ship, but he didn't know which passenger she was. He saw Leia around, and from observing her interactions with others he could infer that she was at least connected (strongly) to the Princess, or even that she was the diplomat aboard the ship, but he didn't gather evidence to a strong enough degree of certainty that she was herself the princess. His comment on the ship was just referring to the fact that he knew that Princess Leia was on the ship, and probably that she had had trouble with the Imperials before.
I agree with the people that say that maybe it was just out of chance, because it was a vague idea, etc. However, just for the hell of it, I think there might two possibilities:
C3PO did not know her, as somebody already mentioned, because his memory got wiped at the end of episode III.
You MAY want to look at this:http://vimeo.com/112993361
C3PO says: "There'll be no escape for the princess this time".
However, this was only in the final version of the movie. In the first versions C3PO actually says: "There'll be no escape for the captain this time".
This means she was hiding in the ship and actually nobody knew she was there. Only R2 ;)
I'm surprised nobody has mentioned this before, but perhaps it's an apocryphal story. At least I can't find reference to it anymore. All I remember now is that I learned about it from one of the pages discussing the detailed changes in the original movie during attempts to de-specialize or restore it from prints.
The way that I've read it, the non-diegetic explanation is that it was a script error caused by a late change to C-3P0's dialogue. In early versions of the script C-3P0's line wasn't "There'll be no escape for the princess this time." The original line was, "There'll be no escape for Captain Antilles this time." The trouble is that Captain Antilles was not a very important character in Star Wars, especially in 1977. He was only in the one scene, and then only long enough for Vader to kill him.
The line was changed and dubbed over to be less confusing to the audience. If I recall correctly, there was a making-of special or interview where Anthony Daniels (the actor who portrayed C-3P0) talked about the difficulty of redubbing that one line, because it was changed after initial screenings and had to be done short notice.
One thing didn't change, though: R2-D2 and C-3P0 weren't Leia's droids, they were Captain Antilles' and that's why they were on board. This is confirmed in Star Wars: Episode III, where Senator Bail Organa gives the droides to Captain Antilles and specifically asks him to wipe C-3P0's memory (a routine operation for droids, as horrifying as that might be). R2-D2 is unique in that his memory is never wiped in the whole saga, which is why he's so... quirky. And also why he knows to do the right thing. R2's not just extremely knowledgeable, he's extremely experienced.
Edit to add: I just noticed that @AlejandroJaramillo did mention this before and I scrolled right past it! His Vimeo link is broken, unfortunately, but you can see the page on archive.org. That still doesn't include the video, but it does allow us to see the title and description.
Deleted Magic
Watch two hours of deleted scenes from the original Star Wars Trilogy (Part 1 of 2)
Searching for that, I was able to find on archive.org a documentary called "Star Wars Deleted Magic Revisited", which doesn't have an IMDB page but I did find it listed on themoviedb.org.
After some searching, I was able to locate a copy of the documentary online. Within the first 15 minutes of the documentary, you can find the screenshot below in Star Wars Deleted Magic Revisited. There are subtitles in the actual documentary because the audio levels are extremely low due to the fact that it was the on-set audio.
Keep watching. When Luke walks away Threepio tells R2 to be careful and not to show the full message, implying he knows what's up and played stupid.
C3PO's restraining bolt put him in safe-mode and prevented him from full memory access. As an aside, R2 also had a restraining bolt, which prevented him from full message playback of Leia's "secret mission" message. Once the bolt was removed, R2 secured the message until the proper recipient (Obi-Wan) could be identified.
