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There are hundreds of threads on drupal.org illustrating the complexity and confusion the new Drupal user experiences in trying to make an informed decision on what image-handling modules to choose to fit the needs of a given site. 1 2 3 4 5 6 7 8 9 10 11 12
So, in response to the many requests for a good overview of this topic in the Handbook - here we go!
There are dozens of ways to handle images in Drupal, and very little in Drupal's core code to even support the various contributed modules (definitions), other than (currently fairly basic) file handling routines.
There is no "one right" image-handling module that fits all the different sites' needs. Some of the variables that need to be taken into account follow.
Please note that this picture will change signficantly with the release of Drupal 7 which will integrate image handling into Drupal core.