Hot off the press! Microsoft just announced today that starting May 22, students buying a PC priced $699 (USD) or more can qualify for a free Xbox 360 4GB console. The only requirements are that you need to have a .edu email address (online purchases), or a valid student ID (brick & mortar stores) to prove you are a student.
Update: A Microsoft employee has clarified that this offer is for high-school and college students only.
It appears that the PC must be a Windows 7 PC, but there are no details if it must be new or can be used. Microsoft states that the end of this promotion will vary from retailer to retailer but the final date for all retailers – if they haven’t ran out of Xbox 360s to give away or they haven’t ended the promotion early – is September 3, 2011; and before purchasing you should check with your retailer if they are participating in this promotion and if you qualify.
Update: According to a Microsoft employee, participating retailers are Dell.com, HP.com, Microsoft Store, and Best Buy. In other words, you need to buy the computer from any of the just-mentioned four stores if you want a free Xbox 360.
Visit this link for more details: http://www.windows.com/freexbox 
*As of now, this is only available in the US, but Microsoft said it will be coming to France and Canada soon.
Update: More details about this offer in Canada have emerged. According to a press release , starting May 27 Canadian students must purchase a Windows 7 HP machine of $599 (CAD) or higher from participating Best Buy or Future Shop to qualify for the free Xbox 360 4GB console.