The Toku genre had robots like this as allies often. To this day you have situations like Navi from Kaizoku Sentai Gokaiger (temperamental, emotional, in ways that make getting information out of him/her harder). More robots than not show emotions that you wouldn't expect to have been included, or are acted upon in a way that inhibits doing their job (any time one gets annoyed and storms off, or Peebo from Choudenshi Bioman being so terrified of Bio Hunter Silver she could hardly do anything). Anri in Kyojuu Tokusou Juspion takes it to "you sure that's supposed to be a robot?" level, looking and acting completely human in every way at almost all times, to the point that you wonder why the writers chose to call her a robot. (However, on one occasion, an evil computer takes her over and makes her attack Juspion.)
At the end of the third season of Agents of S.H.I.E.L.D., Holden Radcliffe creates an android body for his assistant AI, Aida, intending her to be a prototype Life-Model Decoy; she becomes a Fake Guest Star for Season 4. Later, Radcliffe, under the influence of the Darkhold, replaces May with an LMD that no-one recognises as such until Radcliffe's own LMD doppelgänger blurts out that there's more than one quantum brain. Not even LMayD herself recognises herself as an LMD until she notices wires under an injury. After that, S.H.I.E.L.D. has to install LMD detectors in the Playground because it's the only way anyone would recognise an LMD, and even then it's possible to completely miss one - for instance, RoboFitz - by misinterpreting an "LMD DETECTED" warning.
The DRN-series police robots were designed to be as human-like as possible with their "Synthetic Soul" programming. However, the attempt to use them for police duty proved disastrous, and they were all "retired" (it's later revealed that most have been reassigned to Space Station duty). The DRNs were replaced by the utterly logical MX-series robots. When Detective Kennex wakes up after his 2-year coma, he is initially partnered up with an MX, before getting annoyed at the robot and throwing him out of the moving vehicle to be crushed by a truck. Da Chief pulls a DRN out of retirement and forces Kennex to partner up with him. While Kennex and Dorian (the robot's name) are frequently at odds, the partnership proves beneficial, and the two are slowly becoming friends.
Other robots are also shown, including the Sams, middle-aged-looking androids designed as avatars of smart houses, providing personal security. Naturally, a hacker ensures that they go rogue.
Andromeda, the ship, has full-fledged sentience like all High-Guard ships. Indeed, an episode opens with a quote from the High-Guard, where they say "Who would want a ship incapable of loyalty? Or of love?" The episode in question deals with a High-Guard ship that fell in love with its captain and murdered him and its crew with a planet-busting weapon rather than carry out an order to sacrifice herself in a combat situation, upset that he would tell her to do such a thing after all his romantic promises. Maybe that's part of the reason the High-Guard were overrun by the Nietzscheans.
The humanoid Cylons are the definition of robots being ridiculously human — most notably, "robot religion". And robots having robot or half-robot kids. The series then asks all the philosophical questions about the nature of both sides. Doctor Cottle, upon having to do a Caesarian section on a Cylon, bitches her out for her race deciding to be so Ridiculously Human. As he puts it, even if they were gonna insist on having bodies that could pass for a fully functional human, there's no reason why they couldn't have made some basic upgrades to the "plumbing".
It gets weirder: the ancient tribe of humanoid Cylons on Earth One could reproduce sexually and had forgotten resurrection technology, basically becoming human (or at least, mortal). Then they went and built their own mechanical servants, who later nuked their Artificial Human masters.
Caprica reveals that the Colonials could have designed human-looking, but not biological, robots before the Cylon War, but circumstances conspired to have Dr. Graystone's dead daughter stuck with a clunky Centurion body instead.
Buffy the Vampire Slayer: Buffy had to deal with the robotic kidnapper, Ted, and the two sexbots built by Warren Mears: April, and the BuffyBot. Ted is particularly impressive considering he was built in the '50s. April and the Buffybot were both studies in the Uncanny Valley; in fact, April was set up to be a Monster of the Week, but turns out to just be tragic. Buffy stays with her while she shuts down. They don't try to fix her, though, since her whole AI is devoted to Warren and he doesn't want her anymore. And the BuffyBot was milked for all kinds of humor even after they took out the sexbot programming, but her 'death' was carefully designed to have an emotional kick—on the other hand, Buffy's friends treated her terribly when they thought she was the 'bot. Word of God states that the only reason the androids work is because of the Hellmouth's power: they are all Magitek. So they aren't just machines.
Choujin Sentai Jetman's Grey. Looks completely robotic. Acts very humanlike, which includes liking wines, smoking, listening to music and having the closest thing to "love" for fellow Vyram Maria. When you notice that most Vyrams are inhuman, Grey ends up being the resident Noble Demon, who acts quite humanly.
Played for Drama: In "Robot", the K-1 is intended as an experimental machine to do work too dangerous to humans, such as working in radioactive areas or down mines. Yet it also clearly has emotions, displaying love, pain (both physical and emotional), fear, what the Doctor calls an "Oedipus Complex", etcetera. No-one besides Sarah Jane (and by extension the Doctor) notices or respects this, and it leads to the poor thing being driven mad.
Subverted in "The Robots of Death", where a person who thinks that robots should be free of human rule is a maniac and the villain of the story. And is pursued by a secret agent robot. It's a dangerous step to go from "Robots should be free" to "I must kill all my fellow humans to free the robots", but that villain takes it. The robot society is also portrayed as having three classes of robot Dums, which are basic machines with human form but no intelligence; Vocs, which can speak; and Supervocs (like previously mentioned secret agent detective robot) which are intelligent and can make reasoned decisions, possessing something close to free will other than being programmed Three-Laws Compliant and still being much less perceptive than even a below average human. The Supervocs struggle with certain modes of perception (as they can't recognise humans, they have a kludge based on voice patterns, which the villain was able to exploit) and D84, the most intelligent robot in the story and possibly in the whole setting, still makes blatantly obvious logic mistakes in its reasoning that the Doctor points out as being typical robot psychology mistakes.
K-9 often claims to have no emotions or capacity to lie, but he is probably lying. The other characters constantly remark on this.
"Victory of the Daleks" features a robot who's basically just a meek, sensitive, geeky Scotsman. Justified in that a major part of his purpose is that he be indistinguishable from a human.
"The Pandorica Opens"/"The Big Bang" has Auton duplicates posing as Romans based on Amy's memories, including her forgotten fiancé Rory. They're so ridiculously human that the reveal that they're Autons is in fact a plot twist. Rory eventually fights and overcomes his programming, choosing to guard the Pandorica for two thousand years to make up for almost killing Amy.
The new series Cybermen are part human, but actually die if you give them back their emotions. They can't be this trope because being able to feel (being Ridiculously Human Robots) allows them to be horrified at being Cybermen, causing them to die.
"Deep Breath" has a case where the relative humanity of the robot is up for question and significantly alters the outcome of the moral puzzle at the end of the plot if the robot was, like the Doctor said, virtually human, then the Doctor probably convinced it to commit suicide, while if it was still more robot than human, as it insisted, than the Doctor probably directly murdered it.
The Dukes of Hazzard: The episode "Robot P. Coltrane" has the featured character - a robot hired by Boss Hogg to replace the mistake-prone Rosco look very much like a human being, despite the attempt to make it look like a robot.
On Farscape is a class of robot called bioloids, who are Ridiculously Human (or Sebacean, or Scarran, or Banak) for a good reason: they need to infiltrate organizations and replace the people they look like.
Get Smart had Hymie the robot who spoke in stilted robot-speak while looking human. Yoyo, the robot partner of the short-lived 1976 ABC comedy Holmes & Yoyo (played by John Schuck) was similar, actually speaking quite clearly except in certain areas where his speech pattern would repeat due to a faulty program.
Humans: Aside from their uniform bright green eyes, the original model synths are identical to human beings in their appearance. Initially they still lack consciousness, but that changes first with some individuals, then all of them. After that they cannot be distinguished in behavior either, and pass for humans using contacts.
Setting aside the main character and other functional androids in I Am Frankie, there's PEGS1, a hovering egg-shaped robot with a diode panel "face"...who is the comic relief foil to one of the series' main antagonists, worries about things like being fired from his job, and schemes and sneaks like a professional con artist.
The Robot from Lost in Space shows several human emotions and even contemplates suicide on at least one occasion. Verda, the android who appeared in a couple episodes, actually turned into a human when she felt love for the Robinsons.
Mystery Science Theater 3000: Tom Servo and Crow T. Robot are so utterly described by this trope one doesn't know where to start, although the fact that they are often seen eating and drinking seems like a good place. All of this, of course, falls under both the Rule of Funny and the MST3K Mantra.
In The Outer Limits (1963) episode "Demon With a Glass Hand" is Trent, the last man on Earth after all other humans disappear during an alien invasion. He has escaped back in time to our present and it turns out he is a robot created to carry the human race (in digital form) inside him until the aliens are destroyed by a virus released in his own time. He was programmed to think that he was human.
The Outer Limits (1995) episode "Mary 25" also follows this trope with the cybernetic nanny (played by Sofia Shinas) who ends up an unwilling Sex Bot.
Mack Hartford in Power Rangers Operation Overdrive. His father had apparently decided that his biological clock was ticking, and for reasons unknown he decided to get one from a machine shop rather than a womb. Neither the robot in question nor the viewers were aware of his robotic nature until he picked up a computer virus.
Robert's Robots was a comedy series in which most of the cast were robots with ridiculously human characteristics, such as suffering from "condensation forming on my eyes" at emotional moments.
Parodied with Kryten, whose circuitry includes a guilt chip, a belief chip, a good taste chip which is sometimes bypassed by his humor circuits, etc. He also has more depending on which episodes require it: he has a "connoisseur chip" which is never mentioned again after "Legion," etc. He also has a Lie Mode and a Panic Mode.
In the episode "Out of Time", the crew pass through unreality pockets. One of these makes them think that Lister is a droid, which is apparently plausible. He is supposedly an "earlier model":
Rimmer (to Kryten): Well, if he's an earlier model, how come he looks so much more sophisticated than you? Kryten: Sir, just because I have a head shaped like a freak formation of mashed potato does not mean I am unsophisticated! Rimmer: Well, all right, how come he looks more realistically human? Kryten: Humans have always found exact duplicates rather disturbing, sir. The 3000 series was notoriously unpopular.
Kryten states in one later episode that he's quite proud of the character flaws he has (with Lister's help) deliberately developed.
Lister: Kryten, I'm going to teach you how to lie and cheat if it's the last thing I do. I'm going to teach you how to be unpleasant, cruel, and sarcastic. It's the only way to break your programming, man. Make you independent. Kryten: And I'm truly grateful, sir. Don't you think I'd love to be deceitful, unpleasant, and offensive? Those are the human qualities I admire the most! But I just can't do it.
Robots have their own religion, but this is revealed to be a method of control programmed into them by their creators; 'good' robots, who obeyed their human masters unquestioningly, went to Silicon Heaven when they died. Even Kryten has no wish to stop believing in Silicon Heaven, even after he's used his newfound ability to lie to short-circuit another robot by telling him that Silicon Heaven doesn't exist.
Vicky and Vanessa's sibling rivalry on Small Wonder, though Vicky uses Robo Speak and misinterprets things and is generally not an example of this trope.
The robot doppelgängers of the main characters are so ridiculously human that they think they ARE the humans and have a rude awakening when they find out. When the Teal'c one died, he even said to the real Teal'c, "For our father!"
The gynoid Reese is an interesting variation of this, because she has the mind of a whiny little girl in an adult robot body and all the emotions that go with it. Which is how she ended up destroying her planet. She even created "toys" aka Replicators to entertain herself!
The Human-Form Replicators, which were designed from Rees/from which Reese was designed (Depending on which galaxy you're in), are probably the most aggressive things you'll ever encounter - but they are nevertheless believably human. However Fifth is the only one with human emotions, for which his brothers and sisters consider him a flawed creation. When SG-1 manipulates him to dispatch them all, he returns for revenge, falls in love, and even has a creepy stalker obsession with Carter.
Stargate Atlantis: Played for laughs in "Be All My Sins Remember'd". Rodney McKay devises a plan to destroy the Asuran homeworld by introducing a nanite-made weapon, but the "simple" design proves so much more difficult to construct from the ground up than the more complex "humanoid" one (for which the machine already has blueprints) that he creates FRAN, a sentient, living weapon Robot Girl. She enthusiastically helps with the planning and is joyous that she'll be destroyed in the mission, which seriously creeps out McKay.
The "ridiculous" part is mostly averted with Data, as Soong's entire goal was to create an android that was as human as possible, complete with the ability to have sex, should the need arise.
Data created his own daughter, Lal, in an attempt to improve upon his own design. Looking flawlessly human, she developed actual emotions which rapidly overwhelmed her positronic brain, eventually destroying her.
Continuing the trend, Data's creator Dr. Soong created an android to transfer the mind of his wife Juliana into, after her true body was mortally wounded as a result of the Crystalline Entity's attack. Her android body was so perfect that even she still believed she was human, and no-one knew the truth until years later, when she and Data met, and an accident damaged her (rendering her unconscious). Data discovered a holographic interface chip inside her brain, and after installing it in the holodeck, was able to speak to Soong, who explained the full story, pleading with Data to keep it a secret and let her have her humanity. Knowing that this was his own greatest desire, Data chose to honor that request, telling her only, "My father told me that he had only one great love in his life. And that he regretted never telling her how much he cared for her. I am certain he was referring to you."
The holographic Doctor on Star Trek: Voyager was unnecessarily human for a medical expert system. Bedside manner is vital to a doctor, but his was terrible, wiping out that excuse (the real reason is the engineer who created the Doctor program was a raging egomaniac; also, the person in charge of testing his interpersonal relations was Reg Barclay, for whom the description "poor social skills" would be a kind understatement). In an early episode, which was a combination of a holodeck malfunction and a Cuckoo Nest plot, he wonders why it was that he worried about the meaning of his existence. A character responds that it's natural to do so, but the Doctor counters that as a medical program he knows exactly what his purpose is and why he was created.
Cameron shows some very interesting quirks, not the least of which is her odd affinity for ballet. This is discussed in the episode "The Demon Hand", where Sarah talks about how machines cannot do human things like appreciate beauty or create art, and adds that if they could, they won't need to destroy humanity, as they will be human. This monologue is spoken while Cameron is practicing ballet for no readily apparent reason other than because she wants to. She even develops humanlike possessiveness. In "The Brothers of Nablus" she gets upset (well, as upset as she can get) when her leather jacket gets stolen, and even goes so far as to single out the thief who stole said jacket. The episode "Allison from Palmdale" shows her switching over to a normal human personality to disturbing effect. It is made even more disconcerting when we see in flashback that Cameron killed the woman who her personality was based on. The question of her humanity is brought up from time to time within the series as well; Cameron will sometimes existential questions, and seems preoccupied with the idea of suicide and her inability to do so if she loses control of herself, along with worries about her own mental stability. At one point, she even asks if Sarah believes in the Resurrection, as it relates to Cameron's own "redemption" by John Connor, who is humanity's supposed savior.
John Henry qualifies even more so, since he doesn't have Cameron's baggage of being originally designed as a killing machine, and is actively being groomed to be as human as possible. He is shown capable of imaginative play, and loves to play with legos, among other things, and holds genuine affection for the people close to him.
Weaver directly claims to have emotions. Admittedly when she was about to shove a blade through someone's head, but...
The series even gives a good, yet subtle, reason why the Robo Cam is used when Cameron glitches into the Allison personality and forgets she's a machine. Right before that happens, the HUD from her visual input vanishes. With that HUD, she wouldn't have started thinking she was human, which means that the Robo Cam is there to remind the Terminator that it's a machine.
Cheesoid is a cylinder-vacuum / tea-urn-esque contrivance made by an ex-robotics engineer and ex-soup-chef (just go with it) to replace his sense of smell lost in an assault, which inexplicably has rudimentary but quite human AI and some kind of self awareness. And a sense of smell as bad as its creator, only being able to semi-randomly "identify" (generic) Cheese, and "Petril", in a whiny electronic voice. It gets increasingly vocally depressed about its lot, until after a calamitous mistake (serving petrol on toast, and filling a car's tank with brie) it attempts to commit suicide ... by covering itself in cheddar and attempting to light it, succeeding only in creating a philosophical quandary for itself. "Why petril not burn? Why Cheesoid exist?".
Then there's Simon, the contestant on Wordwang who's "from a factory and made from a special metal", and who casually admits that he has killed someone.
Total Recall 2070: Alpha-class prototype androids. This is in explicit contrast with ordinary androids in the series.
In the episode "The Lonely", a convict, alone on an asteroid, is given a robot companion. He becomes so attached he insists she's a real person and needs to be brought on the rocket with them when he's given parole, until the police officer who gave him the robot just destroys it to get him to come along.
An Invoked Trope in the episode "In His Image". Miserable genius Walter Ryder Jr. creates robot lookalike Alan Talbot specifically as an improved version of himself, with a nervous system that will function just like a human one. The chief glitch is Talbot's uncontrollable urge to kill.
Westworld: The hosts were originally merely ridiculously human robots in the style of the original movie, but by the time of the series have been replaced with something closer to Artificial Humans. Indeed, their bleeding is not just for show, as one is saved from death by a crude blood transfusion and in an early scene it's mentioned that MRSA can survive inside their bodies.