The industry standard is Microsoft's Project, a few years ago, Project Managers
Workbench was also a contender. It still may be but I haven't seen it in use for a while.
Neither are open-source.
Serena's OpenProj fills this gap nicely (it was run by Projity until Serena's recent acquisition of Projity). It works on Mac OS X (10.4 here, but can't see any reason it wouldn't work on 10.5 either)
OpenProj
OpenProj is the more feature-rich than most open-source project manager appications, with a number features that you'd find in MS Project. As with most open-source products, it's a bit quirky, but don't let that put you off. Spend 5 minutes with this product and you should get the hang of it. Gantt charts are easy to add, including dragging to implement dependencies between tasks.
Some of the interface seems odd, I'm not sure how much of that is that I'm on a MacBook (so no actual second mouse button although that's usually easy to emulate with holding ⌘. I found it awkward to delete tasks and dependencies (links). This was infuriating as I was learning which way dragging dependencies worked. Work it out first and it's nice and easy after that.
Having a screen split into different, but related panes is becoming common-place nowadays. OpenProj handles this well (better than MS Project in my opinion since it provides standard screen layouts by default. One example is the Gantt chart and spreadsheet in the top half with a resource histogram in the bottom-half. Very useful. Unfortunately, the resource histogram seems to have some odd behaviour. I tested it with 2 resources (Alan and Not Alan). For some reason, Not Alan has a lot more capacity for work than Alan. Maybe it knows something...
Looking at the resource forms showed no differences between the two. So I'm confused. It could just be an auto-zoom feature where the histogram is zoomed to fit the space available. That would be ok given two features which OpenProj doesn't have:
So right now, I'm confused as to how useful that part of it is. Maybe I'll look into it in more detail in future.
As with any Gantt/Project Management tool, learn the difference between fixed duration, fixed resource and fixed work. Fortunately OpenProj can handle all three, making life a lot easier, although I'm not sure if the default can be changed away from fixed duration.
Want more?
There's an interesting business model behind OpenProj. It's based on the popular concept of offering a standard package for free, then charging for additional features. The difference to most is that the standard will suffice for the vast majority of users. I like that. The extensions that require charging for allow you to host the projects with Projity, reporting and progress reporting. Perhaps more important is the extension allowing users to link projects together.
For Windows Users
I've never used it, but Open Workbench looks good for users on Windows.
Other Options
GanttProject is another OS X compatible open-source application. It's much simpler than OpenProj, but does have the advantages of the application being completely open-source, i.e. no commercial add-ons or services. Overall, I found it limited to the point that I didn't feel it worth writing more than a paragraph on. The only reason I could see why a user would use GanttProject instead of OpenProj is if they want protection from whatever the owning company is doing with it. And choosing GanttProject may not be more of a guarantee either.