After reading plenty of desperate forum posts on the upgrade from 1.4.2 to 1.5.0, I was reluctant to upgrade Magento.
I went to Magento Downloader and entered in "magento-core/Mage_All_Latest" in the extension key.
First, Magento Downloader wanted to update itself. Fine.
Second, I checked for updates in Channel: Magento Community Edition, ticked off all the modules to upgrade and then waited an age for everything to finish. I logged out and logged back in, cleared the cache and to my astonishment the upgrade itself went flawlessly.
At this point, the current version of the Extended CCSave extension will no longer work. It needs a simple little work around. After performing the 1.5 update, clear all the caches, and then go to System -> Permissions -> Users. From there click on each user, don't change anything, but click on save. For some reason, saving the configuration gets things working again.
P.S. I've removed some older blog posts that apply to hopelessly out of date Magento code.