There's two major forms of planning software.
- Task level planning
- Project level planning
In the first bucket, you'll find applications like Omnifocus, Things and Wunderlist. These apps will help to manage your list of things to do and offer varying degrees of organization and planning control. Apps in this category are focused on your own list of tasks and don't do as well at tracking things that other people need to do on a joint project.
I personally use Omnifocus. You can create Projects and organize tasks within each project in sequence or treat them as non-sequenced tasks. The app will display the "Next Action" available to you in a project which simplifies the execution side of work as you are able to focus on what needs to be done next to move a project along. Omnifocus follows the "Getting Things Done" model championed by David Allen.
For project level planning you're looking at packages that help manage projects with multiple people or resources involved. These tend to be focused on scheduling tasks that are measured in days vs. hours or minutes. Project level planning tools also provide a great deal of sophistication in managing task dependencies and provide visualization of critical paths through the project. (A critical path is the one that will extend the project duration if any part of the path gets longer.)
Applications in the project planning space include OmniPlanner, GanttProject and Microsoft Project