I know this is less programming related and more time management related, but I value the feedback of the users on this site. I\'m finding myself particularly busy this semester
Microsoft Project within Drop Box also provided an interesting solution if web-access is not needed. This provided excellent timeline management, particularly with task dependencies.
I'm currently evaluating TargetProcess and it seems really nice! It's an Agile project management application so it might do more than what you want.
I highly recommend Request Tracker, as did J.J. It can be hosted yourself, and I believe it runs on Windows. (Since it runs on UNIX, it should run on Mac OS.) I don't know of any Gantt chart functionality for it, but I'll bet there are reports for it that could do that.
I'm just answering to plug Request Tracker, not for the bounty. If for some reason you decide to go with RT, make sure you give J.J. the bounty, as he recommended it first!
Swift To-Do List Standard is one of my preferred application that can manage and track my tasks. It organizes them in a tree structure, has a friendly interface and is ideal for my needs.
http://bstdownload.com/reviews/swift-do-list-standard-7/
We are using Request Tracker. It is free, and has an API.
I used Assembla.com in the past and loved them. But, they aren't free anymore. I have moved my project over to Unfuddle.com which has the same task management features as well as SVN.