Price at $0.99 The Cycloramic app uses the vibration function on your iPhone to rotate it 360° while capturing videos and panoramic photos (coming soon). The only caveat is the phone needs to be placed on a smooth / polished surface. From my time with it, I found that a polished marble or glass surface provides the best results. The app works best with iPhone 5, but not as well on the older iPhones. Get it from the iTunes store here. Do note that the app doesn't work on the iPod Touch as it lacks the vibration function.
If you want to take 360° videos and photos instantly in real time then look into this accessory called Kogeto which is priced at fair $40-50. Get the add on here.