There aren't a lot of apps that specialize in portraits, but Photo Shaper (on sale for US$1.99 on the App Store) does just that.
The app is simplicity itself. Take a photo using the camera controls in the app, or grab something from your Camera Roll. The app mattes a circle around the photo, and gives you a wide choice of backgrounds. When you are happy, you can share the photo with Twitter, Facebook, Instagram or, of course, email.
The results look professional, and I think the app would be good for creating profiles on social networks, or just adding a unique look to any portrait.
The only thing I didn't like is that you have to position and size your photo before the matte appears. It would be more logical to actually see what the image will look like, then make the adjustments. It's not enough of an issue to avoid the app, but editing in-frame would be the best way to do it.
The app requires iOS 4.3 or greater and is optimized for the iPhone 5.