What are some good project-management tools for academics? My advisers are starting to use Basecamp for my project, and I like most of it so far. I am wondering, though, about the arguments for and against Basecamp.
I have been using a mode for Emacs called Org-mode to track my research and do project planning.  See my answer to this question for some of the other capabilities of Org-mode for research.

Org-mode has a number of features that are useful for project planning.  You can set headings as multi-state TODO lists and set scheduled start times or deadlines.  You can also set effort estimates for tasks and generate text based reports via tables or the agenda view, all while inside Org-mode.  The Org-mode manual covers the customizations to these areas and there are a number of tutorials discussing the customization of Org-mode for a variety of tasks.

To generate graphical reports, Org-mode has an export feature for TaskJuggler.  TaskJuggler takes text-based inputs and generates a number of different reports including Gantt charts and resource allocations.  If you do not wish to use Org-mode as the source of your planning, TaskJuggler has its own native format for the text files, highlighted in the manual.

All the tools listed are open source and are actively being developed/maintained.

A potential downside to these tools is that they are primarily text-based.  If you are a visual person who wants a GUI approach to planning/reporting, these tools are probably not suited for you.  Additionally, Emacs has a fairly steep learning curve, so if you are not already using it and do not have the time to become familiar with it, other tools will probably be better suited for you.