When I was in college, one of the most important projects I ever did was a Tetris, in the vein of a project above. It was completely self-directed (not for a class or anything), and took me a few weeks/months. It was the kind of thing I could work on when I had some down-time - or needed to distract myself from schoolwork for a few hours, while still doing something productive.
It wasn't so much a coding challenge as it was a challenge to create, perfect, and integrate every part (every piece of artwork, music, high score list, demo mode, etc.). The end result wasn't a 3D game or even a complicated sidescroller, but it had so much polish, that I'm as proud of it as anything I've ever done.
A completely finished, polished game like that - no matter how simplistic - will not only teach you more, it'll be more impressive to people who matter than any half-completed, unpolished 3D shooter or other, more complicated game.
Challenge yourself to at least take yourself to the "Pac-Man" stage of the above article (as a student, your studies should be your top priority, so I think a finshed, polished sidescroller might be too much). Complete all the graphics. Integrate music and sound effects. Add a demo/attract mode. A high score list. An intro cinematic. A credits scroll.