Bail Organa ordered Raymus Antilles to wipe C-3PO's memory to ensure the true lineage of Leia Organa remained unknown. However, an image of a nine-year-old boy—the droid's maker, Anakin Skywalker—somehow survived the wipe.
Shortly after the Galactic Empire was formed, Bail Organa, in order to protect Princess Leia, had C-3PO's memory wiped clean in order for the droid to not spill any confidential information, especially information related to Leia's true lineage, which would make her a target of the Emperor.
C-3PO's wipe has been the core of many continuity discussions in the Star Wars trilogies, as he didn't recognize Obi-Wan Kenobi in A New Hope but had known him since Kenobi was a Padawan. By wiping his memory, it allowed the leeway necessary to bridge the logic gap created by the previous two prequel films.
He was also evasive with Luke as far as his relationship with Luke's father. C3PO was clearly created from some sort of kit or existing prototype since every protocol droid aside from coloring looks the same. He didn't recognize him because again, they all look the same & it was decades until he saw him again.
C-3PO had been given new parts and a new color. C-3PO himself could not jog anyone's memories as his mind was wiped. Had anyone recognized him, he would have assured them they had never met before. He was also one of a very common protocol droid line; we literally are led to under that there are millions like him.
R2-D2 was present when Padmé gave birth to Leia and Luke, so he knew Luke was Anakin's son – but what he didn't know was that Anakin became Darth Vader. In addition to that, Anakin's fall was surely a painful event in R2-D2's life, one that he definitely wouldn't like to remember or even talk about.
Obi-wan responds to starwars.wikia.com/wiki/Luke_Skywalker saying R2 belongs to him with, “I don't seem to remember ever owning a droid,” which is technically true, because Obi-Wan never did “own” R2 or C-3PO. Obi-Wan then makes a comment that suggests he's more than aware of R2's impressive capabilities.
Instead, the diminutive droid appears to have kept his own counsel, perhaps wary of interfering too much in Luke's personal journey. C-3PO lost those memories, but he remained with Han and Leia's family after Return of the Jedi, so can reasonably be assumed to have learned the truth by eavesdropping.
Since Bail Organa had C-3PO's memory wiped previously in order to prevent him from spilling the secret of Leia's parentage, it could be that this was a semi-regular occurrence for the droid given he couldn't be trusted to keep quiet about things.
secondly, in Legends, R2 was given programming that actually restricted him. from sharing any information with Luke or Leia. about their parents or relation to one another. this was all part of the plan. to conceal this information from the twins.
However, R2-D2's memory is not wiped; as a result, R2-D2 is the only surviving character at the end of the saga who knows the entire story of the Skywalker family. Both R2-D2 and C-3PO end up in the possession of Captain Raymus Antilles (Rohan Nichol) onboard the Tantive IV.
in the Dark Horse comic series star Wars Tales, which is now part of legends, it's revealed that Darth Vader did recognize C. 3PO on Cloud City. when 3PO was shot by Stormtroopers, his parts were brought before Vader. because the Imperials thought he could hold valuable.
Since Obi-Wan and Anakin often fought together, Obi-Wan was friends with R2-D2 as well. This means that although R2-D2 might not have immediately recognized Obi-Wan on Tatooine due to his age, Obi-Wan should have recognized the droid.
C3PO had his memory erased so he doesn't remember at all. And I agree with the above statement about Obi-Wan and R2 having an off set agreement about there friendship. Also Obi-Wan and C3PO had plenty of meetings in the first 3 movies.
After Ashoka and Vader face off in season two (the season finale, I believe), Ashoka has a moment of realization, and Rex has a similar, though less prominent moment like that in a later season. Unfortunately, Rex and Vader never meet again though.
Summary. Anakin's fall to the dark side had a heartbreaking effect on R2-D2, who felt abandoned and ignored by his former master. Star Wars droids like R2-D2 rarely receive emotional depth, making R2's words about Anakin's betrayal even more tragic.
But only a few of the human characters in Star Wars can understand droids; Luke Skywalker wasn't the only one. Obi-Wan Kenobi was another human who could speak Binary, as well as Anakin, who shared the strongest relationship with R2-D2, as seen in the prequel trilogy and Star Wars: The Clone Wars.
Leia's Force abilities and her lack of awareness of her true identity also contributed to Vader's inability to sense their familial connection. Vader's denial of Anakin Skywalker's legacy and his fear of getting hurt again prevented him from realizing the truth about his children until later in the original trilogy.
Darth Vader didn't learn he had a daughter until Return of the Jedi, when he stood before Emperor Palpatine. The Emperor's power probed Luke's mind, attempting to goad him to fall to the dark side, and he discovered Leia's existence. "Sister," the Emperor taunted.
According to Imperial Estimates in Star Wars Inside #87, only about 100 of the Jedi survived Order 66. Most were subsequently hunted down and killed in the years following the Great Jedi Purge.
