Photo Sphere is no longer an Android exclusive. Google released the app for iOS users today, calling it Photo Sphere Camera. It's free, and a nice way to create immersive 360 degree photos.
The app is pretty simple to use. Press the start button and the app will prompt you to move by centering a yellow dot that appears on screen. You'll chase the dot in a complete circle. If you like, you can also point up and down to get a full spherical image of your surroundings. Of course, Google would love for you to upload your images to Google Maps where they can be shared with the public. The image will also be saved to your camera roll, but you can't view it that way as a 360 degree sphere. Instead it appears a really wide panorama. You can view your 360 degree images properly in the Google Photo Sphere app. The Photo Sphere views can also be uploaded to the Google Views site, or embedded in a web page.
The app works really well. During the stitching mode you'll see a little animated man getting all the seams adjusted to make the image smooth.