OmniFocus is a native project manager for Mac, iPhone, and iPad that you can bridge to Basecamp with a product called Spootnik. Macworld recently explored the connection.
Spootnik can sync Basecamp with just, say, an iPhone or iPad (no Mac version is needed as an intermediary), or with every type of Apple-made device you can throw at it. It also provides a separate Web interface for editing your OmniFocus tasks in a browser.You can customize which Basecamp projects and task lists you synchronize, as well as how often Spootnik should sync. Basecamp projects become folders in OmniFocus, and Basecamp task lists become to-do lists under each OmniFocus project folder. If you assign tasks to team members in Basecamp, their names become contexts in OmniFocus for yet more organizational power.