Older than all the examples below is the original Human Torch. He's an android but he completely averted the Robotic Reveal trope that was common in his day by being (synthetically i.e. ceramic bones) human to a cellular level. He was a universal donor and even had genetic material.
SHIELD's Life Model Decoys are meant to be completely indistinguishable from the people for whom they are body-doubles.
Doombots, programmed to act like the real Doctor Doom in his absence. Arguably, it's not very difficult to achieve perfect resemblance to the real thing when the template himself dresses like a robot with a hood and cape...
The resemblance is so perfect, various comic book writers have debated which appearances of Doom were actually Doombots. I.e., they're so good at impersonating Doom, even the writer of the story might not know it's really a Doombot.
Arguably justified to the point of deconstruction by Machine Man, in various Marvel Comics tales. The X-series robots are supposed to be, essentially, Terminators, but Abel Stack is convinced that a robot that can think as well as a human needs to think like a human; when the other fifty robots develop bizarre psychoses and X-51 remains sane, he's proven right, but X-51 also proves useless as a military device. Much later, in Earth X, Uatu the Watcher claims Abel made "Aaron" as an extension of himself, hoping to "live forever" in this way.
...And then Nextwave came along. Aaron Stack's 'sanity', even in the mainstream, can now be said to be somewhat suspect. Ironically, his increasingly 'robot pride' behaviour also came with him not using anything other than his human name as he finds codenames and serial numbers demeaning. This personality shift is the result of a Heroic BSoD following his abduction and then abandonment by the Celestials at the end of his Dark Age series, X-51.
Both versions of The Vision from The Avengers: the original was married to the Scarlet Witch; the new one spent a year traveling around the world finding himself, likes to be called Jonas in private, and is now dating Stature.
The Vision's "brother", Victor Mancha, looks and acts so much like a normal teenager that he himself didn't know he was a robot for years. This was justified considering that he was built as part of an elaborate plot that required him to pass as human for a while. In fact he's built to become more human over time with nanotechnology until the two halves are indistinguishable from each other.
Spider-Man: Peter's parents, Richard and Mary Fitzpatrick-Parker, claimed to not have been killed in an airplane crash, and ended up staying with Peter for a while. It turned out they were robot impostors.
Machine Teen: Title character believed himself to be an Ordinary High-School Student and suffered from frequent seizures. He then finds out he's a robot, his seizures are caused by an internal logic error/feedback loop, and has to escape capture from his father's former boss.
Red Tornado, who assumed the identity of John Smith, married a human woman and adopted a child with her.
The android Hourman, Matthew Tyler. He was even programmed with the 'geneware' of Rex Tyler, the original Hourman.
L-Ron, Maxwell Lord's assistant when he was running the Justice League, fits into this trope perfectly, as does Booster Gold's robot companion Skeets.
The Metal Men are visibly robotic, and don't have human physical needs like nourishment, but are otherwise very much human in their emotions — in fact, they are all more emotional and sentimental than their creator, the stiff, dispassionate Dr. Will Magnus. This was an intentional bit of irony by writer Bob Kanigher.
Superman, during the Silver Age, used to build several robots to assist him. They usually looked so much like himself that it was impossible to tell them apart (which often was the point). The ones he built Post-Crisis were much less lifelike, but still resembled him, except for Kelex who looked quite different.
Just before the New 52 reboot, during The Black Ring storyline Lex Luthor used some kryptonian technology to built himself a Lois Lane robot that looked exactly like the real Lois (except that the robot had some non-human powers).
Shown and lampshaded in issue 4 of Fall Out Toy Works with Tiffany having a cooldown smoke after an argument with Baron.
In the same issue, Mr Moth gets 3000 channels and apparently makes the most of them, what with comparing Toymaker's Heroic BSoD with George Foreman after his match with Muhammad Ali.
Another lampshading in issue 4, when Tiffany finds one of Baron's Mecha-Mooks tending to flowers.
Mega Robo Bros has Alex and Freddy, the protagonists who are a pair of robots who have all the personality of a teenage and young boy, respectively.
There's also Robot 23, the Big Bad of the first book.
NYC Mech is set in an alternate universe where everything is exactly the same as in our world, except everyone's a robot. While these robots have hair, they don't appear very human outwardly, with visible hinges and wires, but they eat, sleep, smoke, have sex, age, etc. That the characters are robots is so immaterial to the plot, one suspects that element was added at the last minute to give the series a unique hook.
Every droid created in the XXIII century in Paperinik New Adventures looks and feels exactly like a human. Despite that, they are just treated as tools. This is later deconstructed when a Well-Intentioned Extremist droid tries to change history to make droids equal to humans. Later,with the "Droids Charter", they finally obtain rights.