Running is a lot of work. That's why the previous version of the Nike+ iPod was a bit of a hassle since you had to have special equipment just to participate in the experience. Apparently Nike agreed.
Now in the App Store is an app called Nike+ GPS which is a stand alone version of the aforementioned application. The $2 selection which you can download here utilizes the iPhone's accelerometer and GPS capabilities (must be running iOS 3.1 or higher), which ditches the need for any additional adapters that it once required...