Negi's outing with Nodoka. Beforehand, he tries claiming it's not a date. Everyone just ignores him. Afterwards Negi again tries to claim it was just a student/teacher outing, but Yue stops him cold with "No. It was a date."
Setsuna's worried denial that her outing with Konoka is Not a Date, despite everyone, including Konoka, treating it like one.
Negi and Asuna going on a date (Type 2) to help Asuna with her shyness issues.
Then there was chapters 251-252, again with Konoka and Setsuna, which sort of inverts this. Setsuna treats it as a a Not a Date, then by the end Konoka turns it into a genuine date by doing a Pactio with Setsuna. One gets the idea that she wasn't really going for the pactio and was simply using as an excuse to make out with Setsuna, who most definitely didn't mind.
Very early in the series, Negi and Konoka have a Type 3, complete with Date Peepers. They were shopping for birthday gifts for Asuna.
Ranma ½: Frequently employed as a plot device and used framed as "Do X for me and I'll go on a date with you."
Sailor Moon: Rei (Sailor Mars) going out to meet another girl at a restaurant, a situation enough like a date that the other Senshi sneak after to spy on her.
Naruto believes Shikamaru and Temari are going out on a date when he sees them walking together. Shikamaru claims he is just escorting Temari. ("Squee!" go the shippers and why Temari would need escorting is not explained.)
When someone asks Naruto if he's on a date with Sakura. Despite the fact that she admitted it was, he said it wasn't. In the anime, it was pretext to speak with Naruto, and in the manga, the two are just sitting on a bench and talking. Naruto only denied that it was a date in fear of offending Sakura.
Love Hina: Several times when Naru and Keitaro are involved, including when both independently went to Kyoto, it was assumed or theorized, by their roommates that it was romantic in nature. Later, when they went out to dinner together, they spent significant time arguing about whether or not it was a date; probably because calling it such results in both of them acting awkwardly.
Soukou No Strain had Sara and Carris going out to find Emily and getting distracted by typical date scenarios. Which makes it even more emotional when he dies shortly after.
Elio is helpfully and secretly given what is obviously a date-oriented itinerary after mentioning he'd like to show Caro around. While everyone assumes they had a fun date, they discover Elio (being a wholesome kid with possibly no frame of reference) showed it to Caro and both followed it innocently like any other mission statement without ever realizing it was supposed to be for a date.
Subaru's and Teana's "vacation" at the same time.
The Wallflower: When Sunako and Kyohei go out Kyohei knows that it's supposed to be a date, having been forced into enacting the guys' latest plan to make Sunako into a lady, but Sunako doesn't and freaks out at any mention of them being on a date. She later talks to Kyohei about the 'date' issue, and the two reach an agreement that it doesn't matter if they call it a date or not; what matters is that they had fun together.
Digimon Adventure 02: Invoked but averted when Yolei/Miyako teasingly suggests to Davis/Daisuke that Kari/Hikari and TK/Takeru are out on a date when both were not present in a group meeting. It turns out that both weren't even at the same place, with the former hanging out with her Digimon and the latter napping.
In the novels, Mikuru invites Kyon to a date, only so he can find out that it was just because of the orders of her superiors, for reasons she (at that point) didn't know but hey, doesn't mean they haven't had fun!
When Haruhi divides The Team up to search the city, Kyon gets paired first with Mikuru and later with Yuki. Haruhi declares, "Kyon, this is not a date!"
Inverted in the 8th novel, when Kyon writes a romantic story about a cute girl he dated for real. Except that it was his little sister's 10 year old friend, who needed him to watch a movie with an age restriction. He wrote about it using misleading technical truths, and selective descriptions to make it sound like a romantic story.
In Kaze no Stigma Kazuma and Ayano aren't going on dates. They're missions. Ayano's father is trying to set them up by paying Kazuma to spend time with her, so it feels all awkward and embarrassing and date-like to Ayano. Kazuma is exploiting the situation like a mad bastard though, and therefore it really isn't a date.
Hayate has gone on several not a dates with several of the characters. Most of the time both characters realize they've been set up on a date by the end of it.
One humorous occasion was when Nagi set up Hayate and Maria on a fake date to lure out a Yandere stalker. She even wrote scripts for them.
There was Hayate and Hinagiku's date to the movies. Once they finally made it into the theater and their hands touched on the arm rests, to two of them finally realized that what they were on could be considered a date. When things fall to pieces (since they were set-up for failure in the first place), Hayate takes her to totally-not-Disneyland-Tokyo where the matter of it being a date is brought up again. This time neither denies it and instead Hinagiku changes the subject to continue the technically-acknowledged date.
Nagi has gone on a date with one of her admirers, all the time denying it was a date. However, she still wound up feeling guilty about it because she really did have a good time. In her own personal reality she kept seeing Hayate's normal behavior as him being hurt and/or jealous.
Wataru also sparked conflicted feelings in his older maid Saki when he took her out to a diner. Turns out he just wanted to talk since, due to a series of misunderstandings, he assumed that she was having an affair with a married man.
Kämpfer has Natsuru going out with Shizuku. He thought that it was a ploy to draw out the White Kampfers despite her insistence throughout that it really was just a date. Up until the end of it where Mikoto goes apeshit when she finds them, he's still in denial.
During the "Hammer Man" sequence in Detective Conan, it looks like Takagi and Satou are on a date, and Satou even asks Takagi to kiss her. Conan sees that they're actually on stakeout, and, with typically lousy timing, interrupts before the kiss can go through. Takagi and Satou were adopting the guise of a young couple to avoid drawing the Hammer Man's suspicions, and Satou even realizes that this interruption will lessen the culprit's apprehension of them even further; would police bother chattering with schoolchildren? Interestingly, taking the disguise of a couple is a common stratagem of Satou's when she's partnered with a male, but she never takes it beyond hand-holding. The kiss offer was her idea of mixing business with pleasure, since she was partnered with Takagi this time. Takagi is very eager to take the next stake-out with Satou. He forgets how common a family name "Satou" is...
In Yu-Gi-Oh!, Anzu and the Pharaoh go on one of these. Yugi, who set them up on it, sees it as a date, but the Pharaoh doesn't. Anzu might, but she denies it being a date to Mai, when she teases them about it.
Yu-Gi-Oh! 5Ds: As the page quote shows, discussed by Rua and Ruka (Leo and Luna in the dub) as Yusei teaches Aki to rollerblade.
Chapter 80 has Shino and Takatoshi buying supplies, while Aria and Hagimura are "conveniently" busy with something else. It later becomes an excuse for them to go out and eat, and it ends with Shino looping her arm around Takatoshi's while the latter doesn't at all seem to mind.
Inverted in chapter 126, Uomi is trying to weasel out the awkward situation with Tsuda (They're buying White Day present) and she told the Student Council members they're on a date.
THE iDOLM@STER - The Producer trying to defuse the bomb Makoto throws in the office as soon as they get back from the amusement park.
In Ratman Shuto and Mirea go see a movie together, and when they meet up with friends afterwards, Shuto tells them it's not a date. It's not so much denial as obliviousness in this case, as Shuto thinks he and Mirea are just friends.
In episode 8 of the Kotoura-san anime, Yuriko forces Manabe to have a date with Haruka as a punishment for his perverted thoughts towards Haruka earlier that episode. Haruka insisted that's not a date, just Manabe's "assigned punishment." The people on the streets disagrees. It's even the title of that episode.
In Young Avengers, Eli and Kate go on a not-date in the park, where they are assaulted by a mugger (kind of). Kate continues to deny that they are on an actual date, much to Eli's annoyance.
In Teen Titans, Beast Boy took Raven out; but when she asked if it was a date, he denied it. If that was the case, why was the issue advertised as "date night", BB? And yes, they're madly in love with each other, but going through too much Angst to admit it.
Back when Robin (Tim Drake) was still dating Arianna, he would occasionally team-up with would-be girlfriend Stephanie Brown to fight criminals on the street. He keeps on insisting that 'it's not a date', but that does not stop Stephanie from shamelessly flirting with him. It also doesn't help that he was giving out mixed messages anyways.
In X-Men Legacy #233, after a grueling battle against Proteus, the first time the two had been fighting on the same team in a long, long time:
Magneto: As I predicted Rogue, it was a great pleasure to fight beside you again.
Rogue: It's not like it was a date, Magnus.
Magneto: No? As close as our kind come, perhaps.
At the end of GI Joe IDW #5, Doc and Quick Kick use their leave time to see a Broadway show. They quickly and forcefully tell Duke and Cover Girl that it's "Not a date!", despite neither Duke or Cover Girl suggesting that it was.
In Undocumented Features, Corwin Ravenhair and Utena Tenjou spend several years Not Dating; when they are told to go have a date, they can't figure out how to start.
In Kyon Big Damn Hero Mikuru tried to deny to Haruhi that going to see a movie with Kyon and Yuki was a date, despite asking Haruhi for permission about this appointment as a date. In truth Haruhi and the rest of the girls explained to Mikuru their plan to acheive a polyamorous relationship, making the attempt to hide it was a date a moot point.
In The Arrangements, Harryand Severus are pretending to be a couple and spend an entire date doing things that they would do "if this was a real date", like sharing a soda at the movie theater and kissing at the top of a Ferris wheel. At the end of the date, they decide that to throw off suspicion, they should continue to see each other on a long term basis, though it's obvious that both of them are only pretending to be pretending.
NanohaAsDivergence, long short story, Vita drags Yuuno out of scene but Hayate said that it was a Date. Talking about Irony, that riddance really turn into a full blown date (Making it Type 2 for both of them), with Vita going straight to Type-A Tsundere mode.
Assumptions: Sure Rainbow. Spending some time with Caramel in Canterlot, having him show you around, admiring views, and introducing yourself to his family with "He's not my boyfriend!", are totally unromantic happenings.
Chapter 26 of A Growing Affection; Hinata wonders if it is a date, and Word of God says Naruto didn't even realize it could be considered a date until they run into the Sand siblings, and Temari and Kankuro make it obvious they think Naruto and Hinata are on a date.
In Pulp Fiction, John Travolta's character is insistent that taking the mob boss's wife out while he's away isn't one of these. Nobody believes him.
Trapped on Draconica: Ben goes to a romantic play with Erowin and no one else. He is the only one not aware that this is a date. This gets him in trouble with Erowin later on, who was unaware that he was unaware.
Live Action TV
Family Matters: The Season 1 episode "The Big Fix," where Laura agrees to go on a "non-date" with Urkel. Despite being told several times that the two really weren't on a date, the nerd gleefully insists otherwise! The non-date was the result of Urkel asking Eddie to do him a favor in return for helping him study for a tough math test. He also holds Eddie's Prince concert tickets as collateral to ensure his date wish comes true.
In the pilot of Lois and Clark, Lois needs an escort to avoid going to Luthor's party alone. After trying every other man she knows, she picks Clark.
Clark: So, this would be like a date?
Lois: A date? Oh, you mean like in Smallville, where you meet my parents and try to give me a hickey in the back of your dad's pickup. No, this is not a date.
Daniel and Vala have one of these the Stargate SG-1 season 10 episode "Memento Mori".
Quote is too funny to leave out:
Vala: Well I don’t mind telling you, I’ve been looking forward to this little date all week.
Daniel: Uhh, I wouldn’t exactly call it a date. It’s…
Vala: Oh, I’ve watched enough of your television to know what a date is. It’s a romantic event, typified by dinner, movie and/or karaoke, and usually culminating in a night of…
Daniel: Uhh, okay, this is definitely not a date.
The Big Bang Theory had one in the first season. Leonard asked out Leslie to get over Penny, but she turned him down. So he asked Penny out, but she misinterpreted it as a going for drinks with the guys. At the end of the night, she asked if it was a date, and he tells her "No! When I go out with a girl, she knows she's been dated."
In Gossip Girl, Dan is accused of having a sexual relationship with his new teacher Rachel Carr. For some reason, they decide the only solution to this problem is to go on Not a Date at a quiet romantic restaurant. Even though it isn't a date, Dan's girlfriend accidentally sees them and gets the wrong idea, and when she decides to take a picture and send it to everybody, hilarity/drama ensues.
Done in Sonny With A Chance where Sonny and Chad go out on a not-date, so she can make a friend of his who dumped her jealous, he's going on it because he doesn't want her dating his friend, and Nico and Grady who missed the entire subplot think that they've admitted the UST and are on an actual date. Later, in season two, when they actually are on a date, they insist that they aren't. For some reason, her friends believe them.
In an episode of Cafe Americain, Holly keeps insisting that her night out with Marcel is not a date until her friend says:
"Is he paying? Did you shave your legs? Then it's a date."
In a first-season episode of House, the titular doctor gets a pair of tickets to go see a Monster Truck rally. Naturally, his first choice is Wilson, who declines for various reasons. His next choice is Cameron.
Cameron: Like a date?
House: Sure. Except for the date part.
Pops up in Sherlock, when the owner of a restaurant is intent on setting a nice, romantic mood at John and Sherlock's table, despite the former's protests. It doesn't help that Sherlock doesn't bother denying it, since he doesn't care what other people think about...well, anything.
A variation in the second episode when Sherlock thinks he's proposing that he and John go on a date, owing to the fact that he has no idea what the term means. John's description of it as an occasion "where two people who like each other go out and have fun" wasn't all that explanatory.
Buffy the Vampire Slayer, ("Crush"). Buffy and Spike are on a stakeout in a secluded location with Spike bringing Buffy various treats. Earlier, Dawn had told Buffy Spike was in love with her, and so she suddenly asked Spike "Is this a date?"
Spike: A d—? Please! A date? You are completely off your bird! I mean... do you want it to be?
In Season 7 "First Date", Buffy is asked out to dinner by Principal Wood, who may or may not be evil. If he is evil then this is an information gathering mission — not a date but Wood is also hot, so if he's normal then this is a date. Unless Buffy is attracted to him because he's evil?
Star Trek: Deep Space Nine: Garak, who has visions of Ziyal presenting his head to her father (Dukat, Garak's archenemy) as a birthday gift, insists that his appointment to visit a Cardassian sauna with Ziyal in the holosuite isn't a date. Quark isn't buying it. Their sauna appointment starts out with him bringing a phaser along for self-defence and her giving him a "The Reason You Suck" Speech but, in the end, Quark is right and Garak is wrong.
Quark: "So, are you cancelling your date with Ziyal?"
Garak: "It's not a date! And how do you know about that anyway?"
Quark: "You're a man. She's a woman. It's a date. And they are my holosuites, after all."
Invoked in the Doctor Who episode Boom Town where Blon tells the Doctor that they are on a date and he hasn't even asked her name. The Doctor points out it's not a date. It's supposed to be her last meal.
The Tenth Doctor and Donna have to repeatedly insist to people that they aren't together. "DoctorDonna" has an entirely different and crucial meaning by the season finale, however.
In the Season Three opener of Teen Wolf Lydia arranges for her and Allison to go on a double date - and then insists to Allison that it's a group thing and not a double date, when Allison says she's not ready to date. She finally admits that it is a double date, but at least, "It's not an orgy."
Kurt and Blaine from Glee have several on- and off- screen not-dates - going for coffee together, dinners at Breadstix, trips to the theatre to see Rent, singing flirty duets together late at night at school - between their meeting in Episode 2x06 and Blaine's Love Epiphany and their subsequent Relationship Upgrade in 2x16. After that point, the not-dates become actual dates, to everyone's great satisfaction. Kurt's best friend assumes his outings with Blaine are dates, and Kurt would like them to be, they're genuinely not.
"Duets". Quinn tells Sam that the dinner at Breadstix they won is not a date. However, she changes her mind during the dinner when Sam tells her she's brave for coming back after everything she dealt with the previous year.
In the very first episode of Friends, Monica insists that her going out with the "wine guy" is not a date, just two people having dinner and not having sex, to which Chandler responds: "Sounds like a date to me."
In the Lost Girl episode Food For Thought, Bo insists that she and Lauren are meeting so that Lauren can help her control her powers, and that it's not a date. Despite their clear mutual attraction, Bo fretting about what to wear for it, and that they are meeting in a bar. Kenzi doesn't buy it.
Major Crimes: When Flynn asks Raydor to accompany him to his daughter's wedding, both of them are quite insistent that it is 'nothing like a date'.
In the musical version of The Wedding Singer, the two not-in-lovebirds get an entire song, titled "Not That Kind of Thing."
Tell the night to save its moonlight
Tell the birds not to sing
Tell the stars in the heavens they've been misaligned
'Cause it's not that kind of thing!
In a Canon side-story of El Goonish Shive, called "Not A Date At The Mall," a man, in return for a favor, buys dinner for his closeted lesbian best friend, with the bisexual female duplicate (don't ask) of her favorite ex-boyfriend mooching. Once the money's changed hands, guess who decides to make himself scarce…
Bun-bun: I just want to clarify. You were there the whole time with Zoë, you weren't drunk or overly medicated or anything, but have no idea whether or not you were on a date?
Bun-bun: Now do you understand, Kiki?
Kiki: Yes, Bun-bun, I now understand why he's a nerdboy.
There's a reason why he's not sure: they didn't mean to do it, they just happened to find a night club in an extremely unlikely place and end up there together.
In Misfile, Ash (the gender-bent main character) is asked to go to the movies with Arthur, one of the other Old Road racers helping her make repairs to the Road. She's insisting that "it's not a date", and is doing it to try to prove that guys and girls can be Just Friends. Arthur thinks it is anyway, and gets upset when Ash shoots down his attempts at making it a date.
Sherry and John "didn't date" for awhile in Out There, awakening Miriam's curiosity  and penchant for shipping. It ended, painlessly, when Sherry decided she was interested in someone else.
Hannelore goes out with Sven just to see what dates are like. Nothing romantic or sexual is expected to happen, and it doesn't.
Marigold doesn't realise Tai's flirting with her and asks her back to her place for an innocent reason which Tai takes as a euphemism.
In Homestuck, Vriska and John have one of these in the afterlife.
Rose insists to Dave that her appointment with Kanaya isn't a date...right up until she realises she was so plastered she lost track of time, prompting a scream of "I FORGOD ABOUT OUR DATE!!!!!!!!!!!!!"
This is played with in Think Before You Think. Jason asks Julia out, and she refuses because she's dating Brian. Then Jason suggests going out anyway as Just Friends, and Julia asks if Brian and Becky can come (who Jason doesn't know yet). During the outing, Julia keeps insisting that it's not a date. Later that night, Julia walks in on Jason and Becky in bed together.
In Teenage Mutant Ninja Turtles (2012), the first time that April, Casey and Irma are shown hanging out together he tells Irma that she shouldn't be chaperoning his and April's date. April replies that they're not on a date. This probably counts as the first time he's explicitly shown romantic interest in her.
Shows up in an episode of the 90s version of Casper the Friendly Ghost, in which Kat goes on what "is so not" a date, and becomes paranoid that Casper is constantly telling her it is (he wasn't there).
Futurama sets this up with a double date, with Kif and Amy alongside Zap Brannigan and a very begrudging Leela. She refers to the encounter as a "half-date" and only agrees to the thing to shut Zap up.
In the WordGirl episode "Have You Seen the Remote?", Tobey and WordGirl had to work together to find Tobey's Master remote. They searched for it the most efficient way possible: by reading together in the library, going to the museum, and eating ice-cream in the park.
This was a running gag in The Emperor's New School, whenever Kuzco and Malina would end up doing something together, Kuzco would call it a date, and Malina would tell him "it's not a date". In the series finale they went on a date.
An episode of Adventure Time where Finn tries to get Bubblegum to go with him to the couples' movie night—while he does have a crush on her, in this case he really just wants to get into the movie. He and Marceline end up going as friends (and, once they find out it's a romantic movie, promptly leaving in disgust to go ride wolves instead).
In Codename: Kids Next Door, when Numbuh One investigates a suspicious party the Delightful Children are holding, he invites Lizzie with him so he wouldn't look suspicious. Numbuh One tells her repeatedly that it isn't a date, until he finally shouts it at the top of his lungs.
Sym-Bionic Titan: Lance and Ilana hang out in the downtown area of Sherman on a school night. They run into a classmate of theirs, who think it is a date. Ilana reminds them that they're (masquerading as) siblings.
Inverted in this story from Kevin Smith's Evening With 2: Evening Harder: His friend, Drawing Flies director Malcolm Ingram came out of the closet to him by telling him about how he had dinner with a guy, then found out half way through it was date. This led to the following question:
Kevin: Well, did you then accept that it was a date?