I'm going to try and use GEGL to allow real-time texture manipulation on an open-source 3D game engine.
What are the most common and most needed operations used on images, textures in game engines?
Well generally image manipulation would be kept to a minimum because it's expensive and, if it's done, it's probably done with a shader.
That said, general things might include color replacement and maybe putting two images together.
However, these are generally not done in real time. Most of the effects are done on what you see and images are already in their ready state.