Luffy gets upset when he is told that rescuing the island will cause everyone to think of him as a hero. He says he likes heroes and looks up to them, but definitely isn't one.
Usopp isn't a coward, he just frequently comes down with various "Can't Do This Specific Thing He's Being Forced To Do Right Now" Diseases.
In the Thriller Bark arc, when Usopp, Chopper, and Nami get caught peeking into Dr. Hogback's lab, Usopp says, "I didn't see anything! Especially not the unfinished zombie!"
Earlier, in a flashback, when Shanks tries to get Buggy to join a celebration, Buggy immediately blurts out he didn't steal anything, when he had secretly acquired a treasure map in the last battle, and was planning to find the treasure and get his own ship.
In a TV Special taking place in Feudal Japan, the wandering monk Zoro casually flips one of Buggy's henchmen into a river and offhandedly says "Oops, I'm sorry. My hand slipped" while clearly smirking. Later on while pretending to work for Buggy, Zoro deliberately attacks Mohji and Richie to protect Vivi. Right afterwards he says "Sorry, my hand slipped", much to Cabaji's annoyance.
In Fever, one guy tries to sneak his dog on a bus by hiding it in his bag. He then asks the bus driver "1300 won without a dog?" The bus driver looks suspicious, but is allowed on anyway.
Part of the Onikakushi arc of Higurashi no Naku Koro ni, while Rena and Mion seem suspicious to Keiichi, he in turn makes them suspicious of him by claiming that he wasn't talking to the police about them when they never asked if that was the case in the first place. In fact, a lot of the stuff in that arc was a suspiciously specific denial, thanks to delusions.
In Full Metal Panic!, Sôsuke has to pretend to be Mizuki's boyfriend (so she can save face in front of her friends). Unfortunately, this is no easy task, considering that Sōsuke has a hard time pretending to be a normal boy due to his being socially inept and only having knowledge about military life. After receiving "coaching" from Mizuki, he tries his best to convince her friends during the outing. His response when they tell him that he looks like he's been through lots of battles and is not at all like Mizuki described him? "You perceive wrongly. I wear common clothing that has no use in battle whatsoever. I feel unimaginable happiness wasting time talking with women. I'm that type of human." Sure. They are not convinced.
Mai-Otome has a scene early on, after Arika and Mashiro have their Green Rocks exploded in an organ accident and Arika has to substitute her Orphan's Plot Trinket. Since this action is very much against the rules, Arika has to feign injuries through most of her classes that require her to have a non-exploded Green Rock. Eventually Shizuru asks her why she's been acting strangely, and Arika responds, "Nothing! I was nowhere near that organ when it went off!" Shizuru pretends she didn't notice and walks off, apparently satisfied. (All she and Natsuki really wanted to know about was the organ, which turns out to be an Ancient Weapon with which they are painfully familiar.)
In Sifr, Lena asks Shirou if he saw the mark on her breast, and he denies seeing or touching it. Naturally, she finds out that he's lying.
Early on in Bleach, Ishida defends Rukia from Renji and Byakuya. When asked by Rukia what he's doing wandering around at night, he answers that he had to go shop at a 24-hour sewing store. "It's not like I took off because I was concerned when I sensed Shinigami energy and brought this bag from home just for an excuse to be outside." Rukia even mentally points out how blatant this lie was.
Yukari makes sure the class knows that the reason they all stayed in her class for the second year (except for Kagura, whom she brought over to win the sports festival) was NOT because she didn't want to learn any new names. (Oh, and please don't change your seating arrangement, either.)
Tomo, cosplaying as a giraffe, stands up during class to say, "I'm not bothering anyone." (link)
"There aren't any dead cats or nothing." says Osaka, trying to convince Nyamo to come to their café during the second culture fest.
Bubblegum Crisis 2040 has Mackie accidentally stumbling upon the Knight Sabers' secret lair and entering the girls locker room. He later tries to defuse the situation by stating that he did NOT see Nene's pink underwear.
Subverted in AIR. In one scene, Hijiri finds Yukito and Kano embracing each other, and wants answers. Yukito tells her, "I know I'm embracing her like this, but it's not what you think! I didn't use alcohol to seduce an innocent little girl and take her to a secluded place to-", even though he really wasn't going to do anything to her (and in fact had been searching for her at Hijiri's request).
Ruby in Rave Master manages to nearly get Haru killed by insistently telling his captors that there isn't one more member of their group who has yet to arrive and, when this lie is seen through, adds that the person who isn't coming definitely isn't the Rave Master.
In the first episode of Keroro Gunsou, after Keroro gets captured by Natsumi and Fuyuki, he goes on to claim he's just an ordinary frog who's larger and smarter than normal, and he's "never even thought about invading Pekopon."
In Ah! My Goddess, Urd confronts Peorth after Peorth's love potion backfires. Peorth says, "I don't know anything about going to your room, taking your medicine, and then trying to monopolize Keiichi's heart." Urd hasn't even asked her the question yet. Of course, Peorth was in a pinch because as a first-class goddess, she's not allowed to lie.
Kyousuke: I wanted to go to the same university as her. It's not that I'm in love with her or anything, it's that I want this comfortable "have-been-together-forever relationship" to continue for as long as possible. And if I’m right beside Miss Average – Manami, I might be able to have the normal life that I yearn for. That was what I thought.
In the anime adaptation, his friend Akagi calls him out over his suspiciously specific denials.
Akagi: So basically she's nothing more than a childhood friend to you, you're not going out with her, you have no feelings for her, but you won't allow other guys to make a move on her?
Simon Brezhnev from Durarara!! will tell you that there is definitely no human meat in their sushi, it's all pure non-human stuff. One wonders why he has to go advertise like that, and the fact that he at some point threatens some Yellow Scarves that he'll make them into sushi doesn't help his case any.
He has also been quoted as saying that Russia Sushi "will not kill you."
Dee and Ryo get taken off a case in one episode of FAKE, leading to this line from Drake:
Drake: Chief! I've managed to apprehend Ben Lloyd, sir! I nabbed him all by myself and definitely not with anyone else's help!
Most of Zero no Tsukaima consists of Louise insisting to everyone in sight that she definitely has no feelings for Saito.
There's an example in one episode of Makai Senki Disgaea, when the Netherland Empresses come in looking for Maharl, who is hiding under the table, and Flonne tells them, "With God as my witness, there is no-one hiding under this table!"
Miyagi "Ah, don't forget, this is totally, completely hypothetical.
Hiroki: "Got it, got it. So what is it?"
Miyagi "Uh, see, there's this kid who just won't leave me alone, keeps following me around and confessing love for me. [...] So if someone showed up and started saying all these things to you, how would you feel?
In one chapter of Wandering Son Shuuichi is looking at some Geisha, and there's a sign that talks about "Apprentice Geisha". Doi comes up and just stares at him for a few seconds, causing this conversations.
Shuu: *blushing and nervous* "I wasn't thinking I wanted to dress like that or something".
Doi: "I didn't say nothing".
D.Gray-Man: Bak definitely, absolutely, certainly did not take those pictures while stalking Lenalee.
In Outbreak Company, the protagonist tries to prove that a girl he found is not a spy from the Kingdom of Bahailam by questioning her. She explains that:
I came here from the east... when I say "the east," I don't mean the Kingdom of Bahailam! I didn't even know that the Kingdom of Bahailam lay to the east! [...] I was never told to do anything like find places that might be secret military installations, and draw them from various angles before sending them home or anything like that! I wasn't going to be paid for every picture or anything...
In Gundam Build Fighters, Tatsuya Yuuki pulls this, when confronted over his identity as Meijin, he claims that he is not the former student council president of Seiho Academy, or the former Captain of their model-building club. His impeccable knowledge of the person he supposedly isn't does not go unnoticed by Sei and Reiji. Especially given his disguise was just a pair of shades.