I unchecked the 2.6.20-16 kernel updates, thinking I could just install the other updates, and the kernel updates installed anyway!
Fortunately it's just my test system, but still.... What's the point of the check boxes in the update manager if it's just going to ignore what I select and install them anyway?
And on top of that, it's still telling me those updates need to be installed, even though they were installed when I unchecked them!
Anyway... if anyone else runs into this problem and can't boot, you can still select the previous 2.6.20-15 kernel from the grub boot menu and that should let you boot. Kind of a pain to have to do that every time you want to boot. Fortunately Linux doesn't need to be restarted very often.
So, to recap:
The current 2.6.20-16 kernel breaks SATA support in Ubuntu Feisty and Mint Cassandra for most Intel ICH4, ICH5 & ICH6 controllers (although apparently not all of them). If you install the auto updates and are running any SATA drives on these controllers it is likely your system will fail to boot (or will boot with lots of problems).
If you run into this problem, hit escape at grub boot and select the previous 2.6.20-15 kernel from the menu and you should be able to get back into your system.
It looks like Debian had similar problems and it has been fixed. Hopefully Ubuntu will be fixed soon.