Project management tools start with the assumption that you are going to build a project first and then add the tasks needed to get the project completed. By creating a series of sequential and parallel tasks, you can more accurately determine the total length of time it should take to complete the project (assuming of course that everything goes on schedule).
An excellent project-centric project management app for the iPad is SG Project, formerly known as Project Pad. This app works in much the same way as larger applications like Microsoft Project, although it is much more streamlined and mobile-friendly.
SG Project, which also runs for $9.99, uses a traditional project management methodology, with normal tasks, milestone tasks, and parent tasks. Tasks can be viewed in a variety of ways, including the Gantt charts we've all come to love. It does a great job for developers on a budget. If you've got a lot of projects and users to manage, you might consider plunking down the $39.99 for SG Project Pro, which expands the functionality of the original SG Project quite a bit.
Another way of handling project management is using the Getting Things Done (GTD) methodology, invented by management consultant David Allen. GTD essentially advocates applying a "do it, delegate it, defer it, drop it" rule to get your inbox empty, which helps determine how to best apply your attention to each task so there's never a sense of being overwhelmed.
If you like the GTD method, you will definitely want to try Omnifocus for iPad. Omnifocus is a task-centric approach to project management, similar to Things for iPad, but has a number of extra features (such as context for tasks and projects) that enable you to manage fairly robust projects. The only caveat is the price tag: $39.99. Like Things, Omnifocus can work with its Mac OS X desktop counterpart. Linux and Windows users don't have to feel entirely left out: an inexpensive third-party service called Spootnik uses WebDAV and a Web interface to sync projects and tasks with Omnifocus from any browser.