The basic plot is that in the centre of Tokyo, is an infamous school called Hope's Peak Academy. Only students selected by the school are allowed to attend. The two main requirements of being invited to be a student are that the potential student must be of High School age, and that the potential must be outstanding in their respective field.
As the school is so famous and so exclusive, graduating from Hope's Peak more or less guarantees the graduate a successful life. The students are considered to be the "hope" of Japan.
The newest class is comprised of fourteen students, all hand-picked by Hope's Peak Academy. Among these students are the "Ultimate Swimmer, Ultimate Baseball Player, but also Ultimate Heir and Ultimate Biker Gang Leader". There is also a fifteenth student, Makoto Naegi, the playable character, who got into Hope's Peak via a prize draw, and therefore has the title "Ultimate Lucky Student."
Upon Naegi entering Hope's Peak though, he finds himself trapped in the school, under a sadistic monochromatic robotic bear called Monobear, along with the other students. Monobear tells the students that they will have to spend the rest of their lives trapped in the school, unless they kill another student. Upon someone being killed, a trial will be held to find the culprit. If the wrong person is voted for as the culprit in a trial, the killer will be allowed to "graduate" and leave the school. The other students will be executed. However, if the correct person is voted for as the killer, the killer will be executed, and the surviving students will continue to live trapped in the school.
The two main parts of gameplay are the investigation stage, which plays like an Ace Attorney game, with the added element that you can choose to spend time with an individual student and give them gifts. This can lead to additional scenes filling out more information about a student's background.
The trial is the other part of the gameplay. These are basically comprised for several mini-games.
Although only released in Japanese, an English translation of Danga Ronpa will be released on the Vita, currently scheduled for release this month.
A sequel, Super Danga Ronpa 2 was released in 2012, but as yet there are no announced plans to release this in English. There are also theories that Danga Ronpa 3 may be in development.
Edited to add:
Dangan Ronpa 2 for the Vita has been announced - http://gematsu.com/2014/02/danganronpa- ... -west-fall. The autumn release isn't as early as it may sound; in that announcement made by a voice actor claiming to play a Dangan Ronpa 2 character, he thought that Dangan Ronpa 2 was the game that had just come out, which indicates that the voice acting has already been done.
On another note, looks like the chances of Zero Escape 3 have dropped - https://twitter.com/Uchikoshi_Eng. Apparently, Spike-Chunsoft aren't interested because both 999 and VLR are in the red in Japan. Uchikoshi himself seems very disappointed.
He is still hoping he will be able to make it via another avenue though. Comparisons to Shenmue 3 have already been made. 