Gantter.com is a great way to start teaching yourself the basics of project planning. This Webware application provides a simplified take on project management, so be aware that you shouldn't lean on it to manage more complex projects. But this is essentially a personal tech project of its creator, Volodymyr Mazepa -- so that if he decided not to continue it for any reason, it could quickly go away.
GanttProject may be a good choice if you need flexibility in how you want to display your task bars in your charts. Still, it's best to keep in mind that you shouldn't go overboard with the colors, lest you create confusion over your project's plan.
jxProject is focused on precision and the minute details of your plan, although the charts it generates can look cluttered, and that ad banner does get distracting. But if you're already comfortable with project management and need to create a plan that shows as much detail as possible, jxProject is worth considering.
OpenProj impressed me with its ability to load most project plan files saved in Microsoft Office Project format. So it's a great alternative if you need to work with someone who's using Office Project, and you don't want to pay for Microsoft's program. OpenProj also stands out for generating the most kinds of charts to represent your project plan.
Open Workbench's split-screen window, which tries to show you as much of your project plan's relevant information at once, lessens the back-and-forth clicking that you have to endure when using other project management software. But jxProject and OpenProj each offer much more in terms of features, like OpenProj's multitude of charts and jxProject's resource optimizer.
So if you're a beginner to project management, break yourself in over at Gantter.com. Then graduate to OpenProj, particularly if you have to work with Microsoft Office Project files. And if you find you need more advanced features (such as extreme precision in allotting tasks to part-time resources, or resources located in different time zones), take on jxProject and consider paying the $20 to kill the banner ads.