Snapseed:
My everyday, go-to editing app. Absolutely amazing in both how much it does (color correction, crops, sharpening, center-focus, tilt-shift, filters, etc) and in how well it does it.
Photoforge2/Photogene2:
More complicated than Snapseed, I use these not for everyday edits, but for when I need something like Layer and Masks support (Photoforge2) or a Clone Stamp (Photogene2). I also use Photoforge2 for its Curves support--great for tweaking color images with fine control. Probably more complicated than most users want.
Phonto:
The only app you'll need for text-on-photos. Add as much as you'd like, import your own fonts (a must for anyone with any interest in typography--no app will have it all), style your text, adjust kerning and line spacing, opacity, and more.
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Diptic:
Create photo sets of multiple images, using over 50 different adjustable layouts. Change border color and width, corner radius, etc. Great for side-by-side photo comparisons as well as more artistic collections.
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(screenshots made with PreviewMaker; side-by-side with Diptic)
Superimpose: Similar to Photoforge2's Layers/Masks options but easier to use in many situations. Most often I use it to isolate an image, delete the surrounding background, and place the remaining image on a new background.
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(Superimpose used to place R2D2 onto a Disney drawing; which was then aged with Snapseed to help blend the two.)
ToonPaint:
Create black-and-white line drawings from your photos (color can be painted back in later if desired). Great controls for adjusting line width, black/white/grey ratios, etc. Much more refined than most "cartoon-ify" apps.
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(ToonPaint used to turn a photo of my dog into a drawing; Photoforge2 used to insert him into the album cover.)
PreviewMaker/iWrapper: A bit of a specialty app, but one I use often when reviewing apps on my site. Both of these use your own screenshots and place them in an image frame for a device of your choosing. I began with PreviewMaker when it was a Cydia-only app; Apple has recently reversed its stance on using iOS device images in screenshot apps so it's now available in the App Store. However, it hasn't been updated for the iPhone 5 yet--so for now I'm using iWrapper. Very similar, but I prefer the workflow of PreviewMaker.
Honorable Mentions:
I just discovered
Glaze, which applies painterly effects to photos. The big plus here is that it does a much better job than most apps. Downside is that the controls aren't very adjustable once you're in a given effect. (You can, however, layer effects.) Here is the shot from above, passed through a Glaze filter.
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(a single pass through one of Glaze's effects.)
ToonCamera does a bit of what ToonPaint does, just not with the same attention to detail. It does, however, give you the option to use it in video mode, which is a very cool feature. It also provides a live preview, so you can see what your sketched images will look like before taking them.
Imgupr is a great way to upload images to Imgur. Easy to navigate and quick, it also makes it simple to copy the IMG codes used in forums like this one. Worth a look if you do a lot of screenshot attachments in places like iMore and don't have a good system yet for posting from your mobile.
GifBoom is a handy way to make animated gifs. It comes with a built-in social aspect that I never use as it's overrun with junior-high kids, but the gif creation works well, letting you use video, images, or text to make your gif. It also provides you with Instagram-style filters, as well as backgrounds, borders, fonts, etc, and can export to the usual facebook/tumblr/sms and so on. There are plenty of other gif apps out there (
Cinemagram is a cool variation that allows you to animate a single part of a video, leaving the rest as a still image) if this one doesn't fit the bill.
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