Americans Hate Tingle: The Professor is disliked by Western fans, who don't gravitate towards the bratty Token Mini-Moe archetype nearly as much as the Japanese fanbase does.
Awesome Art: Despite the fairly simple character designs, everything else about the anime is absolutely gorgeous, even by Kyoto Animation's already high standards. The backgrounds are very highly detailed, seeing real-time perspective shifts in a 2D plane is not uncommon (although some CG is used where it would be otherwise too difficult and expensive to animate by hand, see below), and the frames-per-second rate is remarkably high for this sort of anime.
Awesome Music: Most of the soundtrack consist of beautifully composed orchestral music that perfectly fits the situations of comedy, sadness, madness, or just ordinary moments of everyday.
Delusion Conclusion: An early episode (Chapter 25) sees Yuuko, Mio, and Mai stuck in a broken elevator and undergoing Heroic BSoD. Although later episodes make it clear that they got out eventually, we never actually see how. This resulted in fans speculating that subsequent episodes were actually the Dying Dream of one of the trio stuck in the elevator.
Diagnosed by the Audience: A sizable portion of fans interpret Mai Minakami as autistic thanks to her flat affect, her high intelligence, her inability to pick up on social cues, and her fascination with pranks, the latter of which is often read as a special interest. Such interpretations also portray her hobby of carving statues as a stim.
"Gundere" for Misato, due to being such a massive Tsundere towards Sasahara that she shows her tsun side by shooting him with various kinds of firearms.
"Eh-chan" for Haruna Annaka, for her habit of responding to weird situations with "EHHHHHHH?!".
Friendly Fandoms: The relationship between this show's fandom and Daily Lives of High School Boys's fandom, both due to them being similar in name and due to them sharing the same genre. Both will argue about which show they think is better, but the arguments never get heated, and both fandoms seem to respect each other and their respective shows. If someone has only seen one show and not the other, fans will often urge them to watch the other as well.
Fans in North America and Europe — where Nichijou is one of the most popular comedy anime — are often surprised to hear how badly the anime bombed in Japan and how similarly poorly the manga has sold. The manga ranked 49th in sales for 2011, and the anime lost a lot of money for Kadokawa. It actually got to the point that Funimation decided to take an extra step and re-release the series with an English dub.note Generally speaking, Funimation will always dub their anime, but there are rare cases that they don't due to low expectations on sales and will almost never do dubbed re-releases.
It's also well-liked among Southeast Asian audiences (more particularly Indonesian and Malay) due to subtle references to their language and incorporate of Malay/Indonesian puns into the Japanese language (such as kuma and beruang).
Playing the Helvetica Standard theme over videos featuring Surreal Humor, such as this.
Shake It Saturday.Explanation A counterpart to the "Out of Touch Thursdays" meme surrounding Lucky Star, fans noticed that "Shake It" by Metro Station syncs up uncannily well with the Nichijou anime's OP, leading to a similar edit being created for the sake of being reposted every Saturday by dedicated fans.
Part 96 from Episode 22 where Professor is crying out loud in front of fainted Sakamoto is lately becoming a popular reaction meme, and due to Sakamoto seemingly looked flatted, it has mutated to run that idea for any flattened objects.
Procrastination.Explanation A fan video by prolific web animator Peargor depicting Yuuko, Mio, and Mai reenacting the ending sequence for Joshiraku, complete with Misato shooting Mio in time with the machine gun sounds. The video quickly exploded in popularity thanks to the catchy music and the parody's surprising appropriateness for Nichijou, with many viewers admitting that, true to the video's title, they couldn't stop watching it.
Quirky Work: Despite how the title means "Ordinary Life", the series has a very odd and sometimes surreal sense of humor; the world the characters live in has a lot of oddities of its own, and often seems tailor-made for setups to jokes. There are also several jokes that make more sense to Japanese viewers.
Rainbow Lens: Many fans interpret Nano as a trans allegory based on her insecurity over her physical differences, fear of being exposed as a robot, and wish to be accepted as a normal girl.
Mio unleashing a Curb-Stomp Battle on three people and a goat is probably the most famous scene in the anime, due to both the fluid animation and how unexpected it is.
The entire Part 96 in Episode 22 for its sheer amount of over-the-top hilarity and it's widely regarded as the series' pinnacle.
Spiritual Successor: The show is often viewed by some to be one of the closest things to an anime based on the WarioWare series, since it is a comedic Slice of Life series with a focus on Surreal Humor and wacky characters with unique gimmicks who often find themselves in odd scenarios in an equally odd setting.
In the "Small thoughts" segment of Episode 10, a teacher is talking about how people respond to either praise or punishments. A girl at the distance thinks: "I react to praise... but I never am..."
The scene in Episode 13 where: the Professor allows Nano to go to school is more of a heartwarming moment, but for all the problems Nano deals with, a lot of viewers will feel tears welling up.
If you watched the OVA after the anime, the ending song can be really bitersweet.
Values Dissonance: Sasahara's pretensions of being from nobility despite actually being the son of a farmer doesn't make much sense outside Japan, where owning land is a bigger deal due to being a small country in terms of land mass, and it likely pokes fun at the stereotype of Japanese farmers having inflated self-worth because of this. In the US, at the least, farmers are known for living simpler lives. Amusingly, this also makes it funnier by having him be the polar opposite of that interpretation.
It actually got to the point that Funimation decided to take an extra step and re-release the series with an English dub.note 
