[*Update* As of Feb 18th, 2011, Apple revised the related doc to note:]
"The eligibility period for most Mac Pro computers covered under the ATI X1900XT video card repair extension program has ended..."
(but as of Feb 2011 rev date said)
"If a customer has a video card that is eligible under the program and is exhibiting distorted video, Apple will cover the repair regardless of the Mac Pro product's warranty status."
*Update 2* As of March 22, 2011, Apple revised the related doc to remove the note above. Doc now says only:
"The ATI X1900 XT video card repair extension program has ended.
Resolution
The ATI X1900 video card repair extension program for distorted video ended January 31, 2011.
If you experience distorted video issues, contact Apple or take your affected product to an Apple Authorized Service Provider or Apple Retail Store to determine which service and support options are available. If you plan to visit an Apple Retail store, make a reservation at the Genius Bar using http://www.apple.com/retail/geniusbar/ (available in some countries only)."
(What follows is earlier info from the original Sept. 24th, 2010 news posting, the Apple article has been revised repeatedly since then and is shown just for historical/ref on the original content.)
Over the years here there's been a LOT of posts/articles on ATI X1900 issues (overheating, display artifacts, cooler swaps, dust-cleaning tips, etc) - many added to the Video topics page, graphics card section. Eric sent a FYI that Apple has posted a Kbase doc titled Mac Pro: ATI X1900 XT video card with distorted video that notes certain S/Ns of X1900 cards can qualify for a refund of any repair/replacement costs. (But what about owners that already discarded/replaced these cards and no longer have them to check the S/N.)
"Symptoms
Apple has determined that certain ATI X1900 XT cards sold for use in Mac Pro and Mac Pro (8x) computers between approximately August 2006 and January 2008 may experience distorted video. Affected graphics cards have "V6Z" in the last 4 digits of the card's serial number.
Resolution
If your Mac Pro experiences distorted video and has an ATI X1900 XT card in it, you will need to bring your computer's serial number and the graphics card itself into an Apple Authorized Service Provider or an Apple Retail Store location for verification and to exchange the affected graphics card for a new one. Affected graphics cards have "V6Z" in the last part of the card's serial number. See below for details.
Note: If your Mac Pro has an ATI X1900 XT card but is not exhibiting any signs of distorted video, you do not need to exchange it.
Next Steps:
First, verify that your card has "V6Z" in the last part of the serial number. You will need to remove the graphics card to view the serial number.
1. To remove the graphics card, follow the instructions in the Graphics Card Replacement Instructions.
2. Locate the serial number label on the back of the card, just above the PCIe connector. The label has a 13-digit alphanumeric code below the barcode.
3. Verify that the last four digits contain V6Z as in the image below. If the label is not present or does not contain V6Z, your card is not eligible for this program.
If you believe you have paid for repair or replacement due to this issue, contact Apple regarding a refund.
This program covers affected ATI X1900 XT video cards three years from the original date of purchase or until January 31, 2011, whichever provides longer coverage. Apple will continue to evaluate the repair data and will provide further repair extensions if needed.
This worldwide Apple program does not extend the standard warranty coverage of the Mac Pro."
I underlined/bolded parts of the above for emphasis, and I suspect that like the flawed Nvidia 8600M GT repair program, they may extend the period over time. (But of course that's just my guess.)
FYI: One reader over the weekend wrote he was offered an 8800GT replacement instead - I wondered if they had any Mac X1900XTs left. (Update/FYI: Two readers have said they were asked what OS X version they were using on the Mac Pro - IF pre-Leopard (i.e. Tiger, etc.) the replacement card is X1900XT, IF you say Leopard (10.5.x or later), the 8800GT is replacement reportedly. (Mac 8800GT requires OS X 10.5.2 or later IIRC) - BUT one reader (early Oct. mail) said his replacement card was a Quadro FX4500 (!?). I wonder if anything is consistent anymore.)
Several readers have noted they'd already gotten rid of their X1900s and therefore could not check the S/Ns to see if they qualified. (That was my first reaction to this doc as I suspected many with this issue had already replaced/discarded or sold the original card.)
(Reader reports on the X1900 replacement program are in the Oct. 15th, Oct. 12th, Sept. 29th and Sept. 27th news pages.)
FYI on 2600HD Cards (Feb 2011)
Also noticed in Feb 2011 a doc on a similar issue/exchange program for certain S/N ATI 2600 XT's - see Mac Pro (Early 2008): ATI Radeon HD 2600 XT video card with distorted video or no video
| 
