I use the following iPhone apps to edit my pics:
100 Cameras in 1 - This app is very simple and does not allow editing per se but the application of filters. These filters are arranged in groups like "zen", "serenity", "anxious", "daring", and so on, and the filters in them reflect the moods described. You can then save the file back to the camera roll or share with Facebook/Twitter/Flickr/Smugmug/Dropbox/Instagram/etc
Snapseed - I don't know why I never got this one before, but it was just given away free for a day as part of Apple's "12 Days" promotion. As the poster before me states - it allows for lots of adjustments and borders and faux tilt-shift, etc. You control the intensity of the effects and filters with a simple swipe of the finger. You can then save or share it with all the usual places.
Photoshop Express - A nice free app with some good filters and borders. Slightly less than Snapseed but nice nevertheless. I actually used this to create images that I later made my 2011 Christmas Cards from!
Autostitch - Very cool app which allows you to take a whole series of photos which it then stitches together to make a panorama, or whatever shape image it can! I also have the Panorama 360 app which does a similar job and although it does a decent job, I prefer Autostitch for the way it works.
Color Effects - A nice app, which allows you to choose selective colour in your photos. I used it to great effect with a butterfly on a plant. Using this app I made the whole background black & white, leaving the butterfly itself in colour.
Instagram - Nearly forgot this one! The ultimate in photo sharing. Again, can take pics itself or use from your camera roll. Has some great filters and effects, not to mention its own whole community and sharing service behind it. It can also post your pics directly to Facebook/Flickr/Twitter/Tumblr/Foursquare/etc etc... And it's free!
And just for fun
PocketChris - A handy on-Phone guide to photography. Covers Exposure, Subjects, Depth of Field, White Balance, etc. A nice guide. There is a Basics version which (which I have) is free. The full version has more in it.