I've tried almost every iPhone photo app available. However, I've pared down my toolkit to just a few apps that allow me the creative control I want.
For taking pictures:
Default iPhone camera Of course.
ClearCam This app takes four pictures in fairly rapid succession and then picks the clearest one to save to your pictures. Essential for when it's cold and your freezing and shaking. Really best for still life and landscape. Definitely not good for spontaneous moments.
SneakyPix I like to take candid shots. This app makes your phone look like it's making a call but is secretly snapping shots every few seconds. I've yet to get a good shot from this. You don't realize how important your focus and control is needed to take good iPhone shots until you try to just hold the camera to your ear. I can imagine this would be ideal in situations in which you don't want to attract attention.
For editing: TiltShiftGen I rarely use this app for its intended purpose - creating the miniature world of a TiltShift lens. Instead I use it to create a depth of field. The iPhone tends to take pictures that are in focus in all areas. With this app you can create a sense of visual focus. It's not as good as a slr lens, but gets close. An example of what I'm talking about: http://www.flickr.com/photos/zad...
TSG also has some good, basic contrast and saturation tools as well as the vignette that is typical of Tiltshift apps.
FilterStorm This app has everything. Unfortunately the user experience is a bit rough and the processing seems to take longer than other apps. I use this app for everything from adding exposure - such as when you want to bring back the light in the foreground when you've darkened a picture to highlight the sky - to adjusting curves and saturation. For posting:
Instagram The obvious best for both community and ease of use. The filters are fun to experiment with though sometimes they can frustrate. I'm happily waiting for more improvements to the service. Great team there.
I send every picture to Flickr as well. I'm not giving up on that wonderful team anytime soon.
(I use Picplz to reach out to my friends on the Android platform. I find the Picplz experience uncomfortable to use. It's nice that you can show the entire picture instead of the Instagram square crop, but everything else just doesn't live up to the fun of Instagram.)
I've posted a picture below of my go-to toolkit on my iPhone. I have dozens of other photo apps on my others screens that are rarely used.