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Danganronpa: Trigger-Happy Havoc then.

Published by Spike Chunsoft (which does the Zero Escape franchise, my first pick), Danganronpa is basically the lovechild of Ace Attorney and a rhythm game. It was a huge success in Japan and was translated because of the Let's Play on SomethingAwful. The games match up with 999 as some of my favourite games period.
It's almost impossible to categorize the game along any traditional routes. As a bit of background, the story focuses on Hope's Peak Academy, a location where talented individuals are brought together. They represent the absolute best in their field and are designated by the term "Super High School Level ____" or "Ultimate ____" in English). For example, one character named Celes (Celeste in the translation) is a terrific at games of chance and has swindled insane amounts of money from others. So naturally she's titled "Ultimate Gambler".
Much like the Zero Escape games, it begins with our main character (for the game above, Naegi Makato) losing consciousness. He wakes up at the high school he was just invited to and finds out, to his horror, that they're all locked in and must kill each other in order to escape. But if someone does die, a class investigation is done where everybody tries to find who the murderer was. If the culprit is found, the murderer is executed in a method related to their talent. I've put one in spoilers below.
DEATH (Click Here To Hide/Show Text)
This is for Leon Kutawa, the "SHSL Baseball Star". Anybody who speaks English WILL figure out his murder right away.
And who's at the head of all this? A black and white teddy bear. Named Monokuma (a play on "Monochrome").
Anyways, that's enough about the story. Why did I pick this game? Well, it's the same reason I love the Haruhi Suzumiya franchise: it's a bit of everything. The story itself is pretty horrifying even with its stylized pink blood (done to keep the rating low enough. Bear in mind that this is a game with an M rating). There's a lengthy "Nightmare Fuel" section on TVtropes about every murder and execution. Again, I'll use the first murder here.
Stop ruining the game and play it dammit (Click Here To Hide/Show Text)
And despite all that, it's got an even LONGER "Funny moments" section. It's truly a lot of emotional torque as you get to spend time with what is likely a future murderer or murder victim. You'll come to love someone and then realize that they'll die after. By the way, in the second game the antagonist tells you to not get so attached to video game characters. Too late.

. My favourite character in this game certainly died.
That not enough? Well, it's got an amazing soundtrack. I actually loop a few of them while working on my writing projects. I've put "Discussion - HEAT UP" below. It's used during the class investigation aspect of the game.
Speaking of Class Investigations, these are the flashiest debates you'll ever see. The first image I used? Imagine stuff flying around and you're shooting your counterarguments at it. Okay. Maybe words aren't the best way. Just look at the demo below (Debates start at 5:00 of the first video...then imagine having 5-6 pieces of possible arguments and several possible weaknesses in the argument. They also get a little more subtle than the above).
There's more than that in the investigations, but I don't think there'll be enough space to express how awesome it is to have real time debates.
Finally, this game is extremely meta. Any Ace Attorney fan is likely going to hit the bad end first unless they're savvy. The characters are pretty much living tropes. And by the second game, they pretty much dedicate a character for destroying the fourth wall one brick at a time.
I could go on until I break the character limit...but I'll stop here.