Emulsio (free, but more about that later) takes a shaky video and really smooths it out. Shoot a video of up to 15 minutes in length with your iPhone, iPod touch or iPad and load it into Emulsio. The app fixes horizontal or vertical movement, and even removes some shots that are just too shaky for viewing. One nice feature of the app is that you can see a split screen of the processed and unprocessed video, allowing you to increase the strength of the stabilization routines to fit your needs.
You can then send the photo to your camera roll, email, Facebook, Dropbox, Evernote or iMovie. The processing was very fast on my iPhone 5s -- a twenty second clip was processed in about eight seconds, and it was obviously smoother and more professional looking. You can see a good demo video on the web.