I encountered the white screen error after upgrading one of the blogs I manage from 2.8.x to 3.0.1
After trying to “upgrade automatically”  I got a page that read “Briefly unavailable for scheduled maintenance.” I checked back in a minute then got just a white screen whenever I tried to log into the blog. Though the blog posts themselves, at the base blog site, showed up fine.
I read posts about deleting blank lines in the functions.php and wp-config.php. Link 1 and Link 2.
None of that worked for me.
Weird, I restored both the website files and database from backup but nothing worked. I think this may be because the database structure itself was changed as part of the upgrade that failed before completion.
What finally worked was just to do a manual WordPress Upgrade.
You can read through the steps in the link below this paragraph. But all I did was download the latest upgrade, overwrite all files and folders except for the wp-content folder(copy the files and folders in this folder over individually), and then, in my browser, went back to    “my site.com/blog/wp-admin”    and followed the final steps displayed on the webpage that shows up.
Here is the official link detailing the wordpress upgrade procedure:
http://codex.wordpress.org/Updating_WordPress
Update(Feb 7,2011):
On one of my other blog sites I encountered the same error and was able to move forward by just deleting\moving the .maintenance out of the root of the blog site.