When I was studying assembly at university we were doing small applications all the time. We had tasks like input, output, different sums and sorts (for using loops), 'drawing' some images, like circles, with points, etc.
There also were large projects. The most interesting one is writing a driver. You could take a small device, like mouse, and try to implement a driver for it. If you also add some tests along to find out, for example, where is the problem in case smth is wrong, that would be great experience. Writing a driver properly requires good knowledge of the language, some research on the device and ports, and also pieces of code for testing.
This is project you wouldn't call small, but if you can implement this all than be sure you do know the assembly language!