The GIMP
This is a fully featured image editor with an interesting name - it stands for GNU Image Manipulation Program (apparently). This is an incredibly powerful application with features that rivals professional software like Photoshop. Whilst this software was originally developed for a Linux environment there is a Windows version available; however, in my experience it does not work well on Windows. Nevertheless many people do use it on Windows machines and enjoy its powerful features although for the novice user it's stark interface may take some getting used to.
Paint.net
Whereas the GIMP's interface may take some getting used to Paint.net's is friendly and intuitive, and while Pain.net is not as feature-rich as the GIMP it is still a powerful image manipulation tool with many of the features found in commercial image editing packages. Because it is quick and easy to use it has become my image editor of choice.
IrfanView32
IrfanView is an image viewer which has few editing features, but it is still a worthy inclusion on this list; although, not even as an image viewer (the one built into most versions of Windows is good enough). The reason I have included it is the batch image process feature, with which you can change the format of many files in one go, say from 'bmp' to 'jpeg', rather than open and save each file separately.
Beneton Movie GIF
This application can be used to create animated GIFs. I used it myself to create the animated advert for a friend's website - the one for younilife that you can see at the top right hand of this page. The software works on the same principle as a flipbook: draw the pictures in an image editor such as paint.net; open them all in Beneton Movie GIF; select the order in which they are to be shown and set the length of time each frame is to be shown for. This may sound a little complicated but it is quite intuitive after a while. The software includes some fancy transition features to create dynamic looking animations.
IcoFX
IcoFX is an icon editor. I used it myself to create the favicon for Bloody Computer! (the yellow exclamation mark that you see next the this webpages' URL in the address bar). This software supports all the various Windows icon formats, including those for Vista.