Hagakure, while praying to numerous deities for help, invokes King Kai.
And if Yamada can get a manga/anime/video game reference in somewhere, he'll probably do it. On that note, his name is written as 1-2-3, just like Miyo's adoptive father. Also, he mentions three characters from a manga and refers to them as the Elite Four. He says it sounds cooler that way, even though there's only three characters mentioned.
Not quite anime, manga, or video games, but still worth mentioning: In the official English version, Hifumi cries out "Ia! Ia! Cthulhu Fhtagn!" prior to encountering Alter Ego. One of his Free Time Events mentions author J.G. Ballard. His last words also include him asking if winter is coming.
Another present, the Millenium Prize Problems, are an actual set of seven mathematics problems, six of which still remain unsolved.
The voting screen in the trials bears a significant resemblance to the Monopoly logo.
Upon waking up from his near-murder, Yamada claims that the culprit was Yasu. What he really meant to say was that the culprit was Yasuhiro Taeko, aka Celestia Ludenberg.
In the official English version, Yasuhiro refers to Aoi's plan to fry up some fish and donuts for breakfast and eat till everyone drops as a "Deep Impact style, meteor impact, extinction level event combination of foods."
Owada is trapped in a tiger-themed cage and swirled into butter (or pancake batter); in Little Black Sambo a bunch of tigers chase each other around a rock until they're turned into butter, which is made into pancakes. Taken to another level in the new School Mode, which reveals his underwear has a tiger print.
The Project Zetsubou translation also includes a nod to, of all things, this internet-infamous album cover◊ on the first night when Monokuma says "This big bear has some thangs to do."
In the anime, when Genocider Syo appears for the first time, they say a variation of Soul Eater's opening quote: "A healthy murderer dwells in a healthy body and mind!"
Monokuma's pots of honey he snacks on have to be some kind of reference to Winnie the Pooh.
According to the Something Awful LP, Celes is a walking reference to series like Akagi and Liar Game that deal heavily with extremely high-stakes gambling and competitions. In fact, some of her gambling anecdotes are taken straight out of series like that.
When discussing an incident in middle school during which Naegi helped get a lost crane back into the wild, Maizono invokes a folktale about a man who helps an injured crane, casting herself as the crane who returns as a young woman to repay her benefactor. Her birthday, July 7, also falls on the first day of Tanabata, a festival centered on a story of star-crossed lovers.
In the official localization, after Kirigiri steals Monokuma's special key, he proclaims "Myyy PRECIOUSSS! They stole it!" ala Gollum.
Possibly in Trial 6 when Togami asks if Hagakure is suggesting that Mukuro arrived at the school already dead.
A more blatant example: Sakura's boyfriend Kenichiro (who is outright Kenshiro in the localization), heir to a legendary clan of assassins.
In the Project Zetsubou translation, when Naegi is investigating the burnt sleeve next to the incinerator, Yamada asks if he has a thing for burn victims and that he had just the game for him.
In the official English translation, early in Chapter 1, Toko yells something about not wanting to be dragged further into a "meat dimension."
In the official English translation, Yasuhiro thinks that a Tyrant may be in the bio lab.
Would-be punk rock star Kuwata wears a padlock on a chain around his neck like the one worn by Sid Vicious. Also, in the original game he's mentioned to have previously attended a prestigious school with a top-ranked baseball team, which in supplementary information for Reload is revealed to be named "LL Gakuen"; PL Gakuen is a Real Life high school in Osaka with just this reputation (and speaking of Meaningful Names, it's also the Real LifeMasumi Kuwata's alma mater). Similarly, Ishimaru attended a prominent school called "Kaiseinada," a combination of two Real Life high schools named Kaisei and Nada.
Speaking of the Sex Pistols, one of the best presents the player can give Leon is the Jimmy Decay T-shirt. Jimmy Decay is mostly likely an Expy of Sex Pistols frontman Johnny Rotten.
Calling the fact that Sakura Oogami is called "the Ogre", along with the fact that she is a "super duper high school fighter" a shout out for Baki the Grappler would not qualify alone, as "Ogre" is too general a title for a fighter, but this along with the fact that you get to see her back is the peeking scene, which looks so much like Hanma Yujiro's (actually, the whole Hanma family's) back, sells it.