What iOS camera apps produce realistic HDRs?
I am not sure if this will stay posted since it requires a recommendation.

I use VividHDR and have dumped my desktop program for this gem. 

It uses 5 shots unlike my previous 3 shot and the results are amazing. A user can still make it look unrealistic with tone-mapping settings but other than that I think you should look into.



App features:

Full resolution HDR images.

Universal app

Take 3 or 5 bracketed shots or just leave it to us to decide.
Intelligent algorithms to automatically analyze the scene and get the best exposures to capture details accurately in both highlights and shadows to deliver the best HDR image. You can get 7 stops of additional dynamic range over the regular camera.

Fast processing
vividHDR brackets, shoots and generates your HDR. Snappy fast. All this is done at the full resolution supported by the device and is always ready for the next shot. 

Presets and styles
Control the look and style of your HDR image. Choose from a set of presets obtained from advanced tone mapping techniques. You also have the option to change the preset immediately after capture in the auto-preview mode.

Sharp HDR images
You do not need a tripod to capture great HDR images. Intelligent algorithms automatically compensate for camera shake. Advanced ghost removal techniques ensure that you get sharp images even with moving objects and fluttering leaves in your scene. 

Lazy HDR 
Lazy HDR mode to capture now, style later. Change the presets and edit in non-destructive manner at any point of time for HDRs shot in Lazy HDR mode.

Editing 
Fine editing and post-processing controls for final touches to your HDR images. Controls for basic and advanced editing. 
Basic editing provides control over Brightness, Contrast, Saturation, Temperature and Tint of the image. 
Advanced edits such as Details, Highlights and Shadows allow control over the tone mapping process.

Image formats
Save images in JPEG format with good quality level. Additional option to store images lossless in TIFF format (lossless compression) ensure you don’t lose even those minute details. 

Gallery
Feature to view your HDR images as a single photo, or a thumbnail view for fast browsing and group deleting. Compare your photos 'before-and-after' HDR. It also provides an option to save HDR images to Camera Roll.

Picture information
Supports EXIF and Geo-tag to save the location information. 

Sharing
Share your pictures instantly to Flickr, Facebook and Dropbox, without having to leave the app. You can also E-mail the photo. 



Developers site: http://www.ittiam.com/vividhdr/index.html

Flickr samples: https://www.flickr.com/groups/vividhdr/