Like everyone else here... "me too." I just installed 10.6.3 and my beautiful Mac started giving me the headaches I only get with Windows!
I have something that might help:
In between lockups, I managed to get the Console Messages (HD/Utilities/Console) up. I work in Unix/Linux most of the time, so logs and bash are my happy places. The logs revealed that I had a failing tablet driver:
I/O
warning:
failed to load external entity "/Library/Preferences/
com.pentablet.defaults.xml
Luckily, Wacom provided a way to easily remove the driver (go to the folder in Applications and use the Uninstall option - thanks, Wacom!)
I also rebuilt the LaunchService database from Terminal (this is one line, without the \), though I don't claim that this helped or hurt:
/System/Library/Frameworks/ApplicationServices.framework/\
Frameworks/LaunchServices.framework/Support/lsregister \
-kill -r -domain local -domain system -domain user
http://www.macosxhints.com/article.php?story=20031215144430486
So, go look for something failing ("warnings"). I've read a lot on this subject and it seems that Time Machine and Disk Utility are symptoms - its what they access that is causing the problem (NFS shares, SMB shares, USB drives, external drives), because of a driver or connection made out-of-date by an OS update.
I guess the rule of thumb for OS X users should be: Before you update, go check for new drivers for non-Apple hardware. If you can't find any, remove the old hardware and any drivers it came with, then do the update. If there is an NFS or SMB share causing problems, make sure the host OS has been properly patches.