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.
Redmine - Flexible project management web application
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.
Mantis Bug Tracker - Mantis Bug Tracker is a free and open source, web-based bug tracking system.
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.
SourceForge - The Complete Open-Source and Business Software Platform.