Go to this Seagate support page, scroll down and determine if your Seagate drive is one of the models that is likely to fail. To find out your model, serial number and firmware number consult the 'About this Mac' option under your Apple menu. Then click on 'More Info' and click on the 'Serial-ATA' text to get a list of your drives or drives. If they match the specs of suspect drives from Seagate, you can proceed. To match they must be the same model number and firmware version.
Clicking on the model number of your drive will take you another page that will let you download an ISO image file, which is the firmware update. You can use the Apple Disc Utility to burn a CD of this image. If you are doing this on a Mac Pro, it would be a good idea to slide all the drives out that are not going to be updated. In my case, I had a Western Digital and a Maxtor drive that were not going to be updated, so I removed them.
You then start up your Mac holding the 'C' key down and you should boot from the firmware disc. It will look a lot like DOS (since it is), and you follow the prompts to scan for the drive that needs the update. Then apply the update, making sure you are matching the correct model number on screen to what you have. After a short time you'll be told to exit and shut down. When you are shut down you can restart your Mac, holding the option key down so you can elect to start up on your now updated internal drive. If by chance, the drive you have updated is not a startup drive, then before powering up the Mac go ahead and replace the other hard drives you had taken out.
Once you are at the Mac desktop run System Profiler and check to see if your firmware is updated. On my Barracuda drive I went from SD15 to SD1A which is the newer, repaired firmware.
A couple of caveats: I had a morning full of pain because I could not get my keyboard to recognize the 'option' key being held down so I could choose the startup disk after the update. That was because my keyboard was plugged into my Apple 30" monitor, which acts like a hub. When I moved the keyboard to the front panel USB port all was well again. I'm also told that some of the Apple aluminum keyboards have a similar problem, even when plugged in directly, so you might want to have an old standby keyboard available.
I can't really recommend people try this unless they are very confident, but it is working for many people. Seagate really needs to get better Mac support, and they are going to have to do something about non-Intel Macs. Remember that this fix will not help you if you have an external drive with one of these bad Seagate disks. Seagate is just going to have to come out with a better solution. Finally, and once again, back up any drives you are going to try this update on. Inhale deeply. Cross fingers.