The basic editing functions of the standard iPad Photo app does probably all that most people would want to do with an image. However if you want a special effect or just like manipulating images then there is a very large range of apps that will do that. Most have similar functionality but some do it better than others.
Prices are in $AUS and were correct at time of publication but are subject to change.

Recommended

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Photogene - $2.99 (M-C)

This app has all the usual editing functions and special effects plus more advanced retouch and image adjustment options. There is an interesting collage function which is more like a photo album page creator - whilst photos can be resized within each frame they cannot be moved to other frames. The big benefit of this app is its large array of export options and the ability to bulk upload images to a specific album in Facebook.
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Pixlr-o-matic - Free (M-C)

This app has some very, very basic editing tools but it is really about adding special effects and borders to your images. There are in App purchase options to add additional effects but the standard set that is included in the Free version is quite extensive and would be more than enough for most users. There are about 50 preset effects over 5 categories that can be applied to an image. It also has a variety of export options and sizings.
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Pro HDR - $1.99 (M-C)

High Dynamic Range allows for a greater range of darkness/brightness within the same image. This app will take multiple photos of a scene with contrasting light levels, eg indoors and outdoors through a window, it then stitches the images together so that all parts of the image are within a similar light exposure. There is a free version which created limited resolution images and has a small watermark. The full version is well worth the price tag.
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Snapseed - $5.49 (M-C)

Not the most fully featured image editor or effects creator but the level of creative functionality of both in a combined app is hard to beat. The interface is simple yet very effective with a vertical or horizontal swipe to access functions and slider bars to make adjustments. It therefore is operational within a quick learning curve. If you wanted a good all round app to handle image manipulation then this is it.


Worth Considering

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Adobe Photoshop Express - Free (M)

This comes from a high pedigree but is nothing like the computer version. This is a very basic image editor but is good value for cropping, straightening and basic colour balance adjustments. It is only necessary to have this app on the iPad1 - for some strange reason the image editing functionality that appears in the standard Photo Gallery app on the iPad 2 does not appear on the iPad 1. Don't bother with the in app purchases - there are better options in other apps.
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FX Photo Studio HD - $2.99 (M)

Has some basic editing tools but the strength of this app is almost 200 photo effects and filters which are grouped in 20 categories. Adjustable slider bars control the level of the applied effect to allow the user to manipulate the image to achieve the exact desired effect. It works well and the simple layout is easy to follow.