Google has a program for students, to "help students enter into the world of Open Source software development." They call it "The Summer of Code":
Announcing The Summer of Code - 31/May/2005
We're very excited to launch our newest initiative, the Summer of Code. This program aims to help students enter into the world of Open Source software development. This Summer, allow Google to help you hone your skills on real problems with real programmers. Return to school with some real experience under your belt and some cash in your wallet. By working with some of the most important organizations and foundations in Open Source we think we've put together a program that benefits Open Source, students and computer science. Read more about it and consider taking part!
The "cash in your wallet" part refers to Google's offer to pay $4500 to any student who "successfully completes an open source project by the end of the Summer".
More info in the FAQ. Or, you can be a mentoring organization. How does that work?
Google has teamed up with a number of Open Source related organizations who have agreed to help with the Summer of Code. An applicant applies to work on a project for a given organization. That organization has a designated contact who can approve of the application, monitor the student's progress and sign off that the applicant has completed their work as described in the application.
Organizations already on the list include Ubuntu, the Wine Project, Mono, the Gnome Foundation, the Subversion Project, the Perl Foundation, the Python Software Foundation, and the Apache Software Foundation, some of which have posted ideas students can adopt to work on, if the student has no ideas of his or her own for a project. Or, you can come up with an idea for Google. The deadline to submit a project is June 14.