Apple launched a replacement program for a specific video card on 27-inch iMacs that were sold between May of 2011 and October of 2012.
The "iMac (27-inch): AMD Radeon 6970M Video Card Replacement Program" offers a free video card replacement if your iMac has exhibited particular problems, and Apple will refund your money if you have already paid for a replacement based on these problems.
From the KnowledgeBase article detailing the program:
Apple has determined that some AMD Radeon HD 6970M video cards used in 27-inch iMac computers with 3.1GHz quad-core Intel Core i5 or 3.4GHz quad-core Intel Core i7 processors may fail, causing the computer’s display to appear distorted, white or blue with vertical lines, or to turn black. iMac computers with affected video cards were sold between May 2011 and October 2012.
If your iMac has an AMD Radeon HD 6970M video card and is exhibiting any of the issues described above, choose one of the following options to arrange to have your iMac evaluated:
Before you go in for service, please back up your data. Learn more about backup options.
If the iMac (27-inch) meets these requirements, Apple will replace the video card free of charge for three years after the first retail sale of the computer.
Apple said that you can contact the company if you "believe you have paid for a repair or replacement due to this issue. Apple specified that this does not extend you standard warranty coverage.