I’ve tried some panorama apps on my iPhone 4, but nothing beats Microsoft Photosynth, and it’s free. It’s incredibly simple to use, just turn your camera in a circle and it will automatically capture and stitch the next image. I highly recommend using a tripod or a long stick on the ground to keep your camera steady. The software uses image tracing to stitch the images together, and if your camera moves away from the original spot, it will be more difficult for the software to track your movement due to a change in perspective in a new location. This app is a lot of fun, and people will always wonder why you are spinning in a circle with your phone, and it easily impresses anyone that you can take these with your phone.
Here are some of mine.