Proving that image editing doesn't have to be complicated, Paint.NET brings many of the advanced features of expensive software to a free program. Funnily enough, this is an application whose original team of developers started work on the Paint program that's built into Windows, but this take things to the next level.
You'll probably end up taking no end of photos over Christmas, and some of them might need a little work to make them look their best. Removing red eye is a breeze, as is removing unsightly blemishes from otherwise perfect shots.
This might not be as powerful as the likes of Photoshop, but it includes all of the everyday tools you need, all presented in a wonderfully accessible package that is quick and easy to use. There are all of the usual built-in tools and filters, but there is also scope for extending the capabilities of the program through the use of plugins; there are a huge number available to download from the Paint.NET website.
The beauty of this program is that you can keep things simple if you prefer, but there is also the potential for experimentation with more advanced features without ever feeling overwhelmed.