Which graphics cards are supported by a Late-2009 iMac 27inch? I have the ATI Radeon HD 4850 graphics processor with 512MB of GDDR3 memory installed on an i5 iMac 27inch setup. Given that my current card is malfunctioning and that versions of that card are prohibitively expensive, which cards could I theoretically upgrade to?
According to iFixit.com, you can upgrade the video card to the same one that was in the last 2011 model:


  If you are using the iMac 27" late 2009 or 2010 model for games you
  might want to upgrade your graphics card to the 6 series of the last
  2011 model.
  
  For any other reason this upgrade is not recommended as the power gain
  is only noticeable in games.


Since you have to replace the card, it's definitely a good time to look at an upgrade:


ATI 4850 Card Approx $150 (used) to $400 (new)
ATI Radeon 6970 Card - Approx. $200 (used) to $800 (new) 


The ATI Radeon 5xxx series from the 2010 should works as well, but they are very rare for some reason.  For the price and convenience, I would go with the 6xxx series if upgrading.

If I had the time to search and scour the web for a good deal, I would try to get the 6970 at a good price, but I don't think I would spend the extra money on upgrading a computer that was technically 7 years old with a graphics card that was 5 years old.  Especially so since the graphics upgrade wouldn't be noticeable unless I was gaming.  And if that was the case, I would probably have a console or a PC...but that's just me.

The iFixit link I provided has an excellent step by step on how to replace this card.