Panoramic Photography Apps
There are a large number of applications available to aid in taking panoramic photos using an iPhone.
TripStitch uses the capture-and-stitch method, allowing you to take up to 10 photos in any orientation, and then blends them together as seamlessly as possible to create one large image. 360 Panorama operates in much the same way, and features very simple accelerometer controls that make it easy to continuously capture imagery simply by moving the handset around.
There are also several professional panoramic photography systems out there that don't necessarily use the iPhone itself to capture images. However, these often larger-scale, professional panoramas can still be viewed on the iPhone by using the system's native applications, and offer a more beneficial viewing experience thanks to the iPhone's great screen, its touch interface, and its accelerometer and gyroscopic motion sensing.
PangeaVR is one such professional panoramic system, with free and pro applications, which allow you to view and interact with 3D, 360 degree panoramas that can be downloaded from the internet.
Pixeet 360 is an interesting combination of a professional spherical panoramic photo creator, custom hardware and accelerometer-based iPhone application. The app itself is free, but requires the custom Pixeet fisheye lens to be attached to the iPhone to take the wide-angle shots it uses to create spherical panoramas.