Although you mention not having an interest in math problems, I will mention the idea of Project Euler - math oriented but great exercises. If you don't know much about data structures or algorithms, both are key learning elements. For instance how to create a linked list, a tree, or a graph, how to traverse each, and when to use them. Beyond that, there's so much more. User interfaces, web programming, design patterns...how about create your own project? If you can't think of one, perhaps search an open source repository such as sourceforge or github for either ideas or just simply projects along the lines of your interests, download the source, and look through the code
Do the users have any other ideas of projects I could have a go at. I don't really have much of an interest in game programming or particular math problems, security is something I find interesting though this requires advance knowledge of languages.