There's two, in fact, but I haven't watched either of them so far. The first one (Danganronpa: The Animation) is an adaptation of the first game, which I've heard is not too great because it has to cram hours and hours of gameplay into about twelve 20-minute episodes, so the result is a watered down experience that doesn't add anything versus the source material. (The Ace Attorney anime ran into the same problems, I believe.) Which is great for the developers of course, since it invites more people into the series while still giving them a reason to buy and play the game, but since I started out with the game I have no reason to touch it.
The second is Danganronpa 3, which wraps up the story of the first two games. From what I've heard it's better than the adaptation one, because they had a higher budget and could write their own story, but they also butchered some of the characters and ultimately didn't resolve the plot in a very satisfying way. Have to get around to watching it some day, but I put the "pro" in "procrastination".
I wanted to focus on the games since I've played those (save V3, which just came out and is 2pricey4me) and I know I liked them. They've got a number of glaring flaws, but they're so lovable that it's easily forgiven. They're also really great at character designs (which is good because you can tell they're extremely proud of that). I'd say the characters are the main draw, since you spend a lot of time with the same, slowly dwindling cast of people in a nail-bitingly intense setting. Just when you think you've figured this game out, it throws another curveball at you. Would recommend if you like solving murder cases.
"Have you ever had a dream that you thought was impossible to achieve? Well, some people say nothing is impossible. But I do nothing every day! So you can definitely do it."
--Tofu the dog's infinite wisdom
"British English is easy! Just use an 's' instead of a 'z' and replace 'or' with 'our' and you're dandy." "Do you want pissa our noodles for dinner?" "u better not piss in r noodles m8"
--Classic exchange between Popeychops and John the Late