There are some interesting competitions going on at Google.
First, there's Google Gadget Awards, where you can submit a gadget for Google Desktop or Google Personalized Homepage and win eternal glory and a Google trophy. But you need to know that : "only university, college, or vocational school students with email addresses ending in edu and who live and attend school in the United States are eligible for the Awards."
The categories are also interesting: Most useful gadget (judged by Chris Anderson, Editor-in-Chief of Wired Magazine), Most intelligent gadget (judged by the President of Stanford University), Gadget most likely to help you get a date (judged by Slashdot's Commander Taco), Most addictive gadget and Prettiest gadget. The deadline is November 1, 2006 and the winners will be announced in December. To create a gadget, it's enough to have a basic idea about HTML and JavaScript.
Then, there's Google CodeJam, a competition for the toughest programmers where you can win $10,000 and maybe even a job at Google. The deadline for registration is September 5, 2006. You need to know Java, C++, C#, VB.NET or Python and have a solid Math background.
If you decide one of the contests is right for you, go for it! Good luck!