These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Broken Base: Whether Kuroko is considered an actual member of the Generation of Miracles. Currently, the wikia's stance is that he isn't, due to the fact that he isn't listed as so in multiple points in the manga and in the character bible, among other reasons. It doesn't help that the manga also lists him as being a member of the Generation of Miracles at some other points.
Die for Our Ship: Increasingly for the English fandom, but already very much so in the Japanese fandom.
Kagami for the avid Aomine/Kuroko shippers ; Kuroko for the Kagami/ Himuro shippers.
Not to mention Momoi and Aida who are often pushed to the side in the fandom by their tragic nature of not being guys.
Draco in Leather Pants: Hanamiya is astoundingly popular despite being one of the biggest jerks in the anime. Not only did he make 10th place in the most recent Kuroko no Basket popularity poll, he's also voiced by Jun Fukuyama, a favorite among many anime fans.
Ensemble Dark Horse: Takao is really popular along with Kasamatsu and Miyaji according to the most recent popularity poll.
And now Akashi has taken Kuroko's spot as #1 in the third poll, winning by more than 2,500 votes.
Fan Nickname: Ahomine for Aomine, to go with Kagami's in-universe nickname Bakagami. (Both aho and baka mean "stupid" in different dialects.) Also Kisecchi for Kise.
RIMFIRE is another one for Kagami due to the poorly placed song title in the season 2 opening.
Apparently, Murasakibara is becoming known as 'Titan' or the 'Purple-haired Titan' due to his huge stature; the scene where he's chasing after Izuki makes it seem like a scene from Attack on Titan.
Launcher of a Thousand Ships: Kuroko is paired in a frenzied manner with all the members of the Generation of Miracles - not to mention Kagami, Aida, and Tetsuya #2 it's his namesake dog.
Akashi and his scissors. In his first appearance, he borrows a pair of scissors from Midorima to attack Kagami with. It must have really made an impression on the fans, because in fanart Akashi is always drawn with a pair of scissors, in fanfiction he often has or uses a pair of scissors, etc.
It later became canon that Kise actually does have two sister, which may have added fuel to this meme.
"The only one who can block me..."
"Is it me or they are trying to make Aomine more evil than he really is in the manga?"
Periphery Demographic: The series has a MASSIVE Estrogen Brigade. Actually that can be described as it's main following. 97 percent of fans are female, which is why you see Kuroko no Basuke merchandise in otome magazines and fairs.