Trac - Trac is a project management and bug/issue tracking system. Provides an interface to Subversion and an integrated wiki.
Mantis Bug Tracker - Mantis Bug Tracker is a free and open source, web-based bug tracking system.
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.
osTicket - osTicket is a widely-used open source support ticket system.
Quire - A project management software for teams who dare to dream differently.