Yes I have. Started using Flippity a couple of years ago. Then, after some research I created my own system using Google Sheets.
Although badges act as external motivators, which might cause some people to pause, I have found that they provide a sense of accomplishment and encourage most people to persevere. If interested, I invite you to read my post on the subject - (We don’t need badges, or do we?)
I’ve never implemented a badging system in my classroom, but I would have loved to. I think they would have been a great way to make learning objectives more concrete and would have helped my students reflect on their learning. Also, I totally agree with @mgarcia that while badges are external motivators, they do provide people with a sense of accomplishment. I think that what really makes them work is ensuring that the criteria needed to earn the badge is intrinsically rewarding and enjoyable. If there is a misalignment then I believe that they can become ineffective.
I haven’t tried a badging system in my classroom, but I love Flippity, as @mgarcia mentioned, so I’m excited to look into using it for that.
Our district has a badging system in which teachers can earn credits towards their license renewal for exploring and creating with various platforms, including Formative. Rather than sitting through one-size-fits-all professional development sessions, teachers can choose programs and apps they are interested in, implement them in various ways in their own classroom, and submit details of what they did to earn the badge. Not only have they learned something new to benefit student learning, but it becomes a competition among teachers within the building. Gamifying the learning process appeals to teachers too!