There are plenty of iPhone apps that shoot panorama photos. You take a picture. Move to the left or right, and after you have 3 or 4 images the panorama software stitches the images together.
Now, Occipital is offering 360 Panorama, a different approach to getting wide, or even 360 degree images. The app is dead simple. Click on a button to start the process, then slowly turn left or right. You appear to be taking one continuous image, and as you move you can see the image filling in on a grid. You don't do any stitching, the software does it in nearly real time. You can go wide, or even shoot vertical images. Or you can do both, panning up and down, and moving left or right. The image will fill in. It's pretty cool to watch. When you tap 'save' the image goes to your camera roll.
The app does a lot of processing and therefore needs to run on an iPhone 4 or 3GS. I had good luck using the app. I did have some trouble getting the edges to line up in a complete 360, but I think that is a matter of practice. Boinx released a similar app last week called You Gotta See This!