Write your own web browser
Our cohorts at PC Plus have been particularly prolific with their Linux content recently, explaining how to create your own distro and build a Linux-powered cluster. Now they've turned to programming, with a tutorial on writing a portable web browser with Qt and WebKit. Thanks to the drag-and-drop goodness of Qt Creator, coupled with the embeddability of WebKit, writing a simple browser doesn't require a zillion lines of code. It's a great project if you want to get started with Qt.