During the upgrade to OSX Yosemite on my MacPro I was reaching a white screen with a movable cursor but no other activity. (This screen would appear partway through the progress meter under the Apple logo, after a screen flash.)

This is not the same as "About a minute remaining..." for hours (see below).

Here's two ways to potentially fix it:

• Reboot and hold Option-⌘-P,R to reset PRAM
• Reboot and hold Shift to continue/finish installation in safe mode

The first method didn't work for me, but the second method did. It disables important things like graphic acceleration so the remainder of the installation will be slow - especially so if you're using a 27" display or retina display.

About a minute remaining...

... for hours.

This problem is particularly noticeable if you have any Homebrew managed packages installed. Rest assured it will probably complete. On one of my MBP it took about three hours at the "About a minute remaining" message to complete.

To make sure something is happening hit ⌘L to view the installation logs. You should see a bunch of files getting copied.

Unlike previous OSX installations all of my Homebrew packages were intact after installation. I still needed to install Xcode and the CLI tools which is to be expected.

Update 11/23/2014

For the 10.10.1 Yosemite update I encountered the same white screen problem on my MacPro. In order to complete the installation process after rebooting I finally held down the Shift key during reboot to enter safe mode. The installation of the update completed successfully and I was able to reboot out of safe mode with no problem (though during the reboot from safe mode the white screen did stay up for a few seconds longer than expected).