The main example is the robot society in the show itself, which peddles this trope to the point of comic redundancy, complete with separate-from-human Robot Hospitals, Robot Pornography and even Robot Insane Asylums for Robot Criminals. In a show that's ostensibly a science fiction satire, it fits in quite well as a subtle Running Gag.
Not to mention Jewish Robots who believe that Robot Jesus was constructed, and was a very well programmed robot, but was not their messiah.
Robots even have their own Hell with a Robot Devil. ...Which is located in New Jersey, making it easy to escape.
Seemingly taken to its absurd comedic conclusion with Hedonismbot, a robot grafted into a permanently reclining position with a roman couch as its legs, programmed for no purpose beyond its own earthly pleasures, but then taken to even further extremes once the viewer learns that Hedonismbot is "Your Tax Dollars at Work." In the DVD commentary, the writers kind of lampshade it, pointing out that the funniest things about robots like Hedonism-bot is that someone, somewhere, for some reason, decided to build and program them that way.
Perhaps even better is Roberto, a robot programmed to be an unstable criminal nutjob with a passion for stabbing.
Roberto was built by a research team attempting to create an insane robot. According to Roberto... they failed.
The Don Bot and his Robot Mafia. Not only does a robot mafia exist, but someone built robots for the purpose of working in/running it.
Taken to extremes in the episode where Mom tries to take over the world with a robot uprising. It is revealed that almost every electronic device has a sentient AI, from the television to a ceiling fan and even a musical card. Another episode also had a sentient dumpster.
A robot burn barrel has also appeared, warming its own hands over a smaller burn barrel.
It also bears mentioning that, despite what Fan Fic writers would tell you, they diverge from humans in that two transformers reproducing isn't exactly as exciting or pleasurable as it is for us - what we evolved sex to accomplish, they accomplish by drawing up blueprints and maybe filling out forms for MacGuffin use, which doesn't exactly scream "hot eroticism."
Remarked upon by a scientist disassembling a robot at Itchy and Scratchy Land:
(removing robot's face)
Scientist #1: I really wish they wouldn't scream.
In The Movie, a bomb-dismantling robot cracks under the pressure and shoots itself in the head. Chief Wiggum comments that "he always talked about it, but I never thought he'd go through with it."
Referenced but not used in an episode that involved robot fighting.
Announcer #1: Can robots actually feel pain?
Announcer #2: If so, then we are horrible, horrible people.
This is pretty much the core concept of My Life as a Teenage Robot, featuring a superheroic Do-Anything Robot built to protect the world from threats from outer space, who happens to be programmed with the personality of a girl teenager. Why Dr. Wakeman felt XJ-9 needed such a frequently rebellious, attitude-prone personality is never really explored.
It is implied however that Dr. Wakeman, perhaps even subconsciously, created Jenny as a substitute daughter of sorts, which would explain at least some of her personality traits.
Also, Dr. Wakeman occasionally asks herself the same question.
It is possible Jenny was designed to be human, because her predecessor Armmagedroid had no capacity for independent/human thought, following his orders without question (to destroy all enemy weapons), even attacking his allies/creator to do so. Jenny exploits this weakness in their second encounter and convinces him to self-terminate by using logic to prove he "is a weapon and must be destroyed"
Parodied in Invader Zim with the eponymous character's robot henchman, GIR. "He" eats, drinks, sleeps, cries, parties down and basically acts like a human child. "He" is also assembled from random bits of garbage, dangerously (and often explosively) defective and is the most insane recurring character in the series, which is quite a feat. The only other machines that even speak are a ship that had its owner's personality deliberately downloaded into it for security purposes and Zim's other robotic servants, which also seem to have been infected with his mania.
The apathetic and lazy "Computer," Zim's house AI. Though the least humanoid of robots — he's a glowing green house, after all — he ironically seems to be the most rational of Zim's servants, and thus one of the most "normal" characters on the show.
Speaking of "Computer"s, Dexter's Laboratory AI is a feminine presence in most of the facility, and sometimes surprises Dexter with quips and logic counter to his commands. Where it (she?) is not, there are rejected, obsoleted experiments, that are dejected, if not vengeful, over Dexter's negligence of them.
Mocked in South Park, where AWESOM-O is, according to naive little Butters, a robot buddy. He's actually Cartman in disguise trying to recover an embarrassing video. Butters, a movie studio, and the military all firmly believe he's a robot despite having creativity and breathing air and draw the line only after "AWESOM-O" farts.
The Toyman (as in, the one who first appeared in Superman: The Animated Series) built one of these, and he regretted it. The female android Darci, was based on a doll and built to be his companion. She apparently got tired of being treated like a toy (well, who wouldn't?) and double crossed him; at the end of her initial appearance, a woman - presumably her - was at a train station leaving Metropolis.
However, her desire for a normal life wouldn't last. When both the villain and Superman appeared as guest stars on Static Shock, she was back with Toyman again, who promised to make her a truly human, and actually tried to keep said promise. He had Static's friend Daisy kidnapped and created a "nanite duplicate" of her (sort of a clone), which he downloaded Darci's mind into. Unfortunately, Darci double-crossed him a second time, and this time in a far more evil way, deciding to "break the mold" by killing Daisy. Fortunately, the Toyman was smart enough to install a failsafe this time. He was able to activate it, causing his creation to melt into inert sludge. (She did beg forgiveness and claim she loved him, but he refused to fall for ''that'' again.)
In the future setting of Batman Beyond, building robots like this is illegal, and in the episode "Terry's Friend Dates a Robot", it becomes obvious why. After Terry's geeky friend Howard finds an engineer who is willing to build and sell such a robot on the black market, he buys one that looks like a beautiful woman, whom he names Synthia and has programmed to be "totally into me". Problem is, she is scarily possessive and has superhuman strength. She nearly kills a couple of people who bully Howard, and Batman has to step in. When Howard decides they should see other people, she explodes - literally.
The Robot in the "So Beautiful, So Dangerous" segment of Heavy Metal, while obviously a robot, actively makes a play for the human woman accidentally sucked up into his starship (this being typical robot behavior, according to one of his coworkers). After seducing her he wants to go steady. Also, he shows an essentially flawless grasp of colloquial speech, sarcasm, deceit (with conspiratorial wink), and profanity.
A soft spoken, innocent, and trusting naive robot who doesn't want to hurt anyone and can't resist helping people, Zeta is not only more emotional than most humans on the show, but he's also a better person than most of them. The amazing thing is, he was supposed to be a mindless killing machine, not an Actual Pacifist with a heart of gold, meaning Zeta is one of few examples on this list to be here by accident.
...which makes Zeta the most ridiculous example on this list. Though his appearance has an in-canon explanation, his full range of emotions, human-like body language and expressions don't make sense once you realize he's not supposed to have them. At least everybody else on this list was programmed/designed deliberately to be Ridiculously Human.
Zeta's creator didn't want to be building weapons systems, and included Zeta's conscience in an attempt to subvert his original purpose - "Selig never had the heart for creating a weapon, so he secretly created a module in Zeta without the NSA's knowledge that acted as a conscience, hoping that Zeta would evolve as a person."
Zeta also had to be able to mimic humans enough to infiltrate them for long periods of time - It's stated that he once killed a man, and then posed as him for several months. (Including to his family, and wife.)
Octus from Sym-Bionic Titan. Whenever his human behavior is brought up he appears to get offended and replies with, "I'm not your average robot!"
The Giant RoboGinrei Special appears to follow this when the titular giant robot gets a Nosebleed after seeing a scantily-clad woman. But subverted when it turns out to be strategically-ejected gasoline.
Phineas and Ferb: Seeking a way to defeat his nemesis Perry the Platypus, Dr. Doofenshmirtz discovers in an old newsreel that "the enemy of the platypus...is MAN." So, he builds Norm, a 10 foot robot that looks like a man wearing a suit and that, while trying to demolish Perry, spouts lines like "We should bring our wives next time" and "Secretly, I'm very lonely".
Robotboy. He speaks in robot-tone but he's curious about the human condition and seeks counsel from his interim owner Tommy.
Bot from Team Umizoomi who can eat, cry and feel just like his humanoid companions.
Zane of Ninjago is so ridiculously human that even he didn't know he was a robot until he saw his own blueprints.
In Rick and Morty Rick builds a robot to pass the butter, which is self-aware enough to ask why it exists and to become depressed on learning the reason.
The Humanoids from Il était une fois... Space have, as the name implies, very human aspect -in fact, in one flashback we see how the scientist who build them tells the first it's made in human image-. Many other robots of the same faction, however, just look humanoid.
The title character of Whatever Happened to... Robot Jones? is often portrayed this way. He is attracted to a human girl named Shannon, he is seen consuming an ice slushie with his friends in "Hookie 101", and in "Family Vacation", his need for an oil change is treated like having a Potty Emergency.