What libraries are there to do image editing and image processing with Java?

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Before you search for external libraries, the functionality that you are looking for may already be in the standard runtime library. java.awt.Image has a method to scale images (change their pixel resolution): getScaledInstance (note however that this is not necessarily the best approach for scaling, take a look at the thumbnail scaling demo for an alternative). The package java.awt.image (note the lower-case i) has various classes to crop images, scale them (AreaAveragingScaleFilter), rotate / flip / mirror them (AffineTransformOp) and apply convolution kernel filters (ConvolveOp, to blur, sharpen, detect edges etc.).

Sun's own Java image processing library JAI (Java Advanced Imaging)—offers quite a few image operations, many of them optimized for speed with native code. A pure Java implementation is available as well.
ImageJ is not a library but a program with a plugin concept, but maybe you can reuse the plugins.
Java Vision Toolkit
JIGL - Java Imaging and Graphics Library
JXPM—image processing library for Personal Java
PMIW: Poor Man's Imaging Wrapper—encapsulates a number of imaging libraries and offers their combined functionality under the roof of one API.
JIU (Java Imaging Utilities)—image processing library, also includes its own codecs (disclosure: written by the author of this FAQ).

I maintain a similar list on the JIU site.