Ayuri: Kay displays completely human behavior within a panel of being activated.
The titular character, Pilot, and also quite a few of the characters in Pilot are like this. Androids such as Norman are very easy to be mistaken as human beings, and as for Pilot, aside from his grey skin, one could easily mistake him for a human.
Ping from MegaTokyo sleeps like an actual human when she's in idle mode, can use the chemical energy from sugar to recharge her batteries, and in one chapter, she angrily tells Piro that she has real feelings even though these feelings are simulated. However, she does have a couple of robotic quirks: when she sees Piro all mopey because he couldn't wind up the courage to call Kimiko, Ping misrecognizes his posture and attitude as being rejected by Kimiko, and suddenly goes into Genki Girl mode. Not bad for a PlayStation 2 accessory. She is also been explicitly stated to be "fully functional," and Word of God has even implied that she has a working uterus.
Some of the most memorable characters in the comic Freefall are robots, many of whom show quite human behavior.
Florence Ambrose: Can we at least try to solve this logically before you robots go all emotional?
The webcomic Nine Planets Without Intelligent Life has a cast consisting of nothing but Ridiculously Human Robots, who eat (and gain/lose weight somehow), drink (and get drunk), feel pain and even date and wed each other. It justifies this by explaining that the humans that built them before humans went extinct wanted to make sure robots could better appreciate and interact with normally humans-only pleasantries, such as theme restaurants.
Pintsize seems to have emotions (mostly schadenfreude and lust) and has even gone through a phase of questioning his gender/sexuality.
"AnthroPCs" in general seem to be designed to combine the functions of a desktop/laptop computer, a pet, and (inevitably) a child.
Apparently Roombas are fully functional enough to find mates and reproduce. In fairness, everyone agreed in-universe that that one was weird.
Pintsize ended up with a laser because a government semi tried to mate with a Best Buy semi.
Word of God: "No one is sure who decided it would be a good idea to give AnthroPCs libido, but everyone agrees it would be more trouble than it's worth to remove it. Besides, the horny little bastards would revolt."
Later on, Momo shows a more human and well rounded personality than most of the other cast, including things as complex as sadness for the plight of the first AI (it was stuck in a box for several years while it was tested) to gratitude and love for humans in general for accepting AI's so welcomingly.
Lie Bot and Vlad from Achewood are both robots which are constantly lying, and talking about Make-outs respectively. Vlad, for no reason at all, has an accent.
On the world of Terra, in Magical Misfits, magic makes artificial intelligences like computers, or robots, living things.
Robots in S.S.D.D seem prone to developing into this unless they are designed with caps on their intelligence and personality or if they don't have them they usually have their memories erased every few months.
Various robots display human-like personalites, and human-like comical incompetence. For example, they hide their presence by labeling their spare part storage room as "NO spare robot parts". Their gatekeeper, Doorbot, was fooled by Annie's Paper-Thin Disguise. And the Guardbots attempting to apprehend Annie are completely flummoxed when she runs away from them. A possible explanation for this arises later: the robots are magitek.
A later arc features a Robot King (who draws emotions on 'his' face with markers), a Robot Society, in turmoil, nonetheless. And let's not even count the fact that the robots apparently have true emotions, are capable of being moved by a painting and upset by a wreckage. Magitek at its finest...
Warmech from 8-Bit Theater is convinced it is an example of this, despite being a walking tank.
Robot News Anchor: A massive search party is searching for the missing Secret Angel Princess-Princess as well as GOFOTRON's right arm. Our prayers go out for them both. But more for Secret Angel since she's a person and GOFOTRON's arm is a thing. But then again, I'm a thing, so who cares. Nobody cares about us things. [beat] Robot News Anchor: I hate you all.
The Muses, twelve breathtakingly advanced humanoid clanks created for the Storm King two hundred years ago.
Master Payne: The Muses were renowned as miraculous, beautiful machines — but few would believe they were truly aware. And maybe they're not. It would certainly be easier to create machines that merely simulate emotion. However ... even if her grief is artificial, it is destroying her.
Agatha's dingbots (pocketwatch-sized clanks she builds as assistants) are intelligent enough to carry out complex commands, show love and loyalty towards their creator, and even remember old grudges.
Dr. Robot in The Incredible and Awe Inspiring Serial Adventures of the Amazing Plama-Man not only seems to have an almost sociopathic sense of humor, but is also evil, both of which are decidedly human traits.
Some of the robots in Schlock Mercenary are like this, especially the construction drones. They can even feel pain, although that's justified:
Drone: "Pain will help us cut maintenance costs." You didn't mention how much it would hurt.
Bob and George plays this trope even straighter than Mega Man in the name of comedy with robots, Mega Man in particular, being capable of eating ice cream, getting drunk and vomiting.
Nicki in Times Like This acts human enough to be actually mistaken for a human.
Stephanie in Groovy, Kinda is a robot that can actually drink... and get drunk.
Never Mind the Gap is an unusually hard and justified example. The comic is about a town inhabited by a mix of humans and Ridiculously Human Robots, which are almost exactly like humans personality-wise (though obviously robotic in appearance). They have to go through a very human-like childhood as they mature, and can become romantically involved with each other and with humans. The explanation is that in this universe, AI researchers found no way to make an AI with human-level intelligence except for modelling the AI very closely on the human mind, and also giving it a fairly humanoid body. Every attempt to make a less human-like AI either failed or resulted in insanity. Intelligent robots were initially found to be useful for a variety of tasks, which explains why people bothered to build them, but eventually, predictably, they wanted to be treated as people; the comic is set in a time and place where they've largely won this fight, and so now they no longer need to be "useful," as such, other than as equal members of society. It's notable that there are also non-human-like "smart" devices and non-humanoid robots in this setting, but their intelligence and abilities are limited. The Ridiculously Human Robots are realistic in other ways — for instance, the complexities and limitations of their humanoid bodies, and the associated maintenance costs, are explicitly addressed. The possibility of non-human robots is contemplated with the uplifted octopi, who could possibly make robots modeled after their own mind.
Tentadora from Zoophobia: At first, she looks like she might be human or at least, some humanoid creature, knowing the setting. But then she changes to a more robotic look, revealing herself to be a robot with a ridiculously humanoid form.
The robot characters from Supertron are this in spades.
Ugofandian from Marooned has built a ridiculously Martian robot.
There turns out to be a few of these in The Far Side Of Utopia; Ila certainly counts, as does Mium, though both have fairly obvious parculiar tendencies. Averted (or perhaps played really straight...) with the only character that looks a robot (Mir) seemingly not being a robot.