Awesome Ego: Sora is impossibly arrogant, confident that there's not a soul alive that could beat him at games, aside from his kid sister. But he's not just full of hot air as he lives up all of his boasts and is an exceptional Guile Hero.
"There Is A Reason", the theme song from The Movie. It's a touching and beautiful piece that almost comes off as a love song for Riku and Shuvi.
Base-Breaking Character: The main duo, particularly Sora. Fans love their knack for unorthodox and brilliant strategies, and consider them well-developed characters with realistic flaws and shortcomings. Their detractors, however, may argue that they're overpowered wish fulfillment characters, and are turned off by Sora's perverted tendencies and Shiro's attraction toward her adoptive brother.
Broken Base: The fanservice. Part of the fanbase is fine with it, believing that it's at an acceptable level and/or is Played for Laughs, so it's not there for fanservice's sake, while another part finds it to be excessive and is turned off.
Crazy Awesome: If Blank's fight against Kurami didn't tip you off on how batshit insane game rules can get, then the one against Jibril definitely will.
Sora betting his own freaking existence! Kurami outright calls him insane.
Designated Monkey: Stephanie Dola. She's become Sora and Shiro's pet princess and personal toy, but it's hard not to feel sorry for her given how hard she's trying to help Imanity.
Black Bullet as well due to both stories having a male main-character with a loli-girl sidekick; helped by the fact that they were both released during the Spring 2014 anime season.
Follow the Leader: A small number of people with exceptional abilities are, after responding to a message, summoned to another world where everything is decided with games and they group up with the lowest-tier nation in order to help them climb the ladder? Where have we heard that before?
Hilarious in Hindsight: Sora uses Persona 4 (or better said, "Pers*na" to convince Shiro that they didn't go to back to Tokyo, but are in a video game, something they can handle. While the fourth Persona game (which is pictured) takes place in the small town of Inaba, the fifth game takes place in Tokyo, and has a Shut In party member who's also an avid gamer.
The ending of the Materialization Shiritori game in Episode 6, has Sora going outrageously far with the game. He removes the Earth's outer layers to expose the core to make Jibril fall towards it, followed by removing Coulombs Forcenote the electrostatic attraction between particles causing the entire universe to collapse now that there's nothing holding it together and unleashing a hypernova of fifty billion Celsius that rivals the Big Bang!
Episode 9 where Sora bets away his own existence in one of the most elaborate Thanatos Gambits, just to get Kurami and Feel to see that he's genuine.
Les Yay: The relationship between Fil and Kurami appears to be "girlfriends" but it's more like a mother-daughter thing.
Stephanie and Kurami most fit The Woobie aspect of it, making viewers want to give them hugs. In fact, all of them to an extent, because they all have their quirkiness and individual appeal.
Schwi is not only an example of this trope (being a small, cute and innocent girl with an endearing love for Riku) but her research into "the heart" apparently led to her creating personality routines for it (such as Little Sister Heroine).
Moral Event Horizon: Many fans turned on Jibril when she killed Shuvi in the movie. Her fans believe the action was in character for her, and as such, don't hold it against her, while her detractors often see it as an uncomfortable reminder that while her past deeds during the war were Played for Laughs, she was never a good person.
One True Threesome: Considering Sora and Shiro's extreme co-dependence on each other, it's virtually impossible that Stephanie and Sora have a private relationship without including Shiro in the mix.
The Woobie: Kurami. Despite being a crybaby by nature, she's unwilling to admit how much she's suffered as a slave to the Nilvalen family- she alludes to Feel sometimes having to be distant from her for the sake of Feel's public image, but Feel's noting that Kurami cries whenever Feel takes her eyes off her might indicate that Kurami's bottling up her pain. While Kurami's friendship with Feel is definitely a bright spot in her life, she has trouble accepting it due to a mix of low self-esteem and guilt over what associating with a slave and planning on ending slavery forever is costing Feel.
Woolseyism: The translation for the terms thrown around during the game in episode 6 must have required some serious thinking to get meaningful terms in English (out of Japanese) which still form the required chain. Suffice to say, the translators did it brilliantly.
The German version instead establishes that the words used can be in any language (which is canon considering Sora specifically asks if it's okay), so Sora can use the English words "Suitcases" and "Earth's Outer Core" at one point.