Based on our record, Mantis Bug Tracker seems to be more popular. It has been mentiond 3 times since March 2021. We are tracking product recommendations and mentions on various public social media platforms and blogs. They can help you identify which product is more popular and what people think of it.
I use https://mantisbt.org/ Mantis, no need of Docker. Source: over 2 years ago
Perhaps Mantis Bug Tracker? Admittedly I've never installed/used it myself, but looks to be built using PHP so might work on shared hosting. Source: almost 3 years ago
We use MantisBT at work. Simple, just a trouble ticket tracker, no bells and whistles, which is exactly what we wanted (along with a REST API I was able to integrate it into the app so that users don't even have to open the site). Source: about 3 years ago
Redmine - Flexible project management web application
Jira - The #1 software development tool used by agile teams. Jira Software is built for every member of your software team to plan, track, and release great software.
Asana - Asana project management is an effort to re-imagine how we work together, through modern productivity software. Fast and versatile, Asana helps individuals and groups get more done.
GitLab - Create, review and deploy code together with GitLab open source git repo management software | GitLab
Trello - Infinitely flexible. Incredibly easy to use. Great mobile apps. It's free. Trello keeps track of everything, from the big picture to the minute details.
Trac - Trac is a project management and bug/issue tracking system. Provides an interface to Subversion and an integrated wiki.