Comment Botball/ACSL (Score 1) 842
You might check around to see if your area has a botball competition. The website www.botball.com has a list of all the teams, so you can get an idea of whether or not it's in your area. Basically, you build robots using legos and other specified materials, though you have a limitation on them and the robots must push balls around a small court against another team. You also have to program your robots, generally in C, so that they know what to do and how to move. It's very time-intensive and unless the students have an idea of what they're doing, it's probably not worth it to start a team. On the other hand, it is a lot of fun, and certainly gives nerds an opportunity to hang out.
Another possibility, that I also found enjoyable, was the American Computer Science League (ACSL) competition. It's a national competition, though schools from other countries do participate. It runs throughout the school year, with an All-Star competition Memorial Day weekend. Students take both written exams on computer topics, like bit strings and boolean algebra, and write programs. Both have time constraints and the written portions in particular require studying. It is good practice for those who intend to go into CS in college. You can look at the rules and see sample problems at www.acsl.org. This really is my first recommendation.