This past April, the ESO (European Organization for Astronomical Research in the Southern Hemisphere) announced the winners of the Catch a Star! competition for students. This is the 5th year of this competition, so we can hope that there will be more years to come and we'll catch the competition in progress next time.
The Catch a Star! competition has a category for student research, in particular in areas of astronomy that are suitable for the large ESO telescopes. There's also a lottery competition that also involves a project paper, but in this case perhaps in a large group. Finally, there's an art competition (and here's the 2007 art gallery).
The big prizes are for research projects, and involve trips to ESO observatories in Chile, Austria, Germany, and Spain.
Here's an older article from Innovations Report that describes the launch of the competition, expanding on some of the details I got from the ESO site. Another article, this one from Science In School, reports on the results of the competition. The article has some of the artwork. It also describes the winning team's successful eclipse observations in Chile, in what could have been bad observation weather.