Widely used project management tool. Has many plugins.
LibrePlan is a web based project portfolio management system. The community version is free and enables managing projects portfolio, tasks, resources, resource planning etc.
Taiga is an open source agile project management tool. Supports both Scrum and Kanban agile methodologies.
New open source project management tool, supports agile, integrates with git and svn. Has gantt views.
Interesting project that uses MantisBT to manage the tasks. CodevTT provides project management and timetracking of projects. It can alert on delays in projects.
Open source agile based (Scrum and Kanban) project and portfolio management.
Mantis Bug Tracker
Supports Scrum agile.