there are a lot of photography apps out there, either for editing for for taking the picture. The most common photography app is definitely Instagram. The one reason that people like that app a lot would be the social network, but i feel like its not so much about the photography itself.
The one app that intrigued me while i was reading about good camera apps would be Camera+.
I have never used this app but it looks good, practical, and easy to use for a quick picture. It advertises having 16 scene modes to bring out the best in your photo so you can match up the lighting in your scene with the mode. There have been a lot of complaints that there is no video feature on the app, but i like it that way.