For students who need extra challenges, there are many local, national and international competitions available. Here are a few pages with links to some of these competitions:
Cogito.org has the best list of competitions for students in middle school or high school. The site is maintained by the John Hopkins Center for Talented youth. While the competitions are listed alphabetically rather than by subject area or grade level, they do list the sponsoring organization and grade level on the main listing. There are almost 200 competitions to choose from!
Hoagie’s Gifted: Contests and Awards is another source for a listing of competitions. In addition to links to more information, the site provides a brief description of each of the competitions. The site was updated just a few days before this post was entered, so the information is current.
The Illinois Association for Gifted Children: Students page contains links to a variety of special programs and competitions designed for gifted students. In the upper right corner of the page is a link to gifted programs which they say are sponsored by the University of Illinois. However, some of the programs on that page are sponsored by other Illinois colleges and universities.