Danganronpa is a game franchise with only three canon ones. But there are, I believe, like two other ones by the same creator with some of the same characters.
Danganronpa takes place in a high school called Hopes Peak Academy, which is meant for the gifted. In this world, the gifted are referred to as 'Ultimates'. These people are the best in their field, and there could only be one of them. So, for example, you could have an Ultimate Writer or an Ultimate Marathon Runner.
16 students are admitted to Hope's Peak Academy, but instead of having a normal high-school experience, they pretty much get kidnapped and locked up in this place with no escape or contact with the outside world. Anyways, they meet this bear who tells them that they're trapped in a killing game, and there's only two (but there's another one) ways out. One way is to be one of the final survivors. The other is to kill someone and not get found out. The last is to figure out who the mastermind is.
It continues like that for all of the games pretty much.