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."
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!