For people wanting to dabble in HDR beyond what Apple provides on iOS I'd suggest a look at HDR3 from developer Christopher Herbon. This US$0.99 app takes three different exposures in rapid succession, which are then combined to give you much more dynamic range. Bright areas of the photo won't be overexposed, dimmer parts won't be lost in shadow.
The app supports a full 8 megapixel resolution on newer iPhones, and has some built-in image stabilization. After the image is taken, there are adjustments available for saturation, temperature, gamma, sharpness, brightness and contrast. You can crop the image, and add from a selection of frames.
Taking three rapid exposures is more than most HDR apps offer, including Apple. Usually, two exposures are taken, but that extra exposure can make a difference in a really high-contrast situation.
I tested the app against Apple's built-in HDR feature, and found HDR3 better in almost all situations. I also compared it to another favorite of mine, ProHDR. The two apps had similar results. In some situations, even with only 2 exposures, ProHDR did quite well. In other lighting environments, HDR3 had a slight edge.
HDR3 is a bit slower at rendering photos due to the extra image, but the results look nice. Some people don't like HDR at all, because it can oversaturate colors making the image look garish, but that is in the hands of the photographer. There is plenty of control here to create as realistic, or as unrealistic an image as you would like.
There is a free version of the app you can try, but it is limited to 1 megapixel images and it leaves a watermark.
HDR3 is a universal app, it requires iOS 6 and is optimized for the iPhone 5.