Ive been using Dermandars Panorama App since its inception. It blows away the competition (including options from Google, Apple and Microsoft) on price, ease of use and the quality of the final product.
Whether youre shooting 180 or 360 degree panoramic images, as long as your hand is semi-steady youll get bonafide great results with squared edges (unlike Apples native camera app/mode).
But the best part of this app is that you can scroll through (or use the internal gyroscope) the resulting image as if it were really curved around your body. You can even share the results and have friends experience the same immersion even if they dont have the app. (Dermandar hosts the uploaded image on its servers).
Stills can be downloaded to your camera roll for free. The most recent version of the app now allows for HD stills and Videos of the immersive experience to be downloadable if you pony up for the additional in-app purchases. ($2)
Every time I use this app I end up being an unwitting evangelist for it. People always inquire how Im getting the results, while others with more professional equipment are surprised I can get such good results from an iPhone.
$RUM about DMD Panorama, v5.4