[Added 2006-10-15: Another potential fix here...]
In addition to the potential solutions posted here, here, and here, the following are some additional things to try when battling the dreaded 0x8ddd0009 error from Windows Update / Microsoft Update. These suggestions come from comments that others have posted to the aforementioned blog entires, as well as new ideas compiled from various community discussions.
In many cases, update sessions that ultimately result in the 0x8ddd0009 error cause high CPU utilization prior to erroring out. There is suspicion that on older hardware, this can cause "time outs" or other undesirable quirks with the Windows Update / Microsoft Update services / websites. Presumably, pruning some of the applications and services that are running prior to attempting to use Windows Update / Microsoft Update can help in this. Disabling antivirus applications in particular (read on) seems to help. It may be that rebooting the system, exiting as many applications as possible (including those running in the systray, by the clock) when the system comes back up, and then stopping unnecessary services(*) before trying Windows Update / Microsoft Update will do the trick for some people.
* - Of course, it helps to know what services are necessary and what services are merely "nice to have". The following may be of some assistance in determining this. Note that I have NOT reviewed these links; I encountered them when trying to determine what happened to BlackViper's site (blackviper.com); appears he forgot to pay his domain name registration fee and lost it... You may have some luck with Archive.org's archives of the site... Anyway, on to the links:
Services Guide for Windows XP
Windows XP Services Tweak Guide
Windows 2000 Services Tweak guide
One person reported that uninstalling the .NET Framework 2.0 and rebooting took care of the problem.
Another reported that registering / re-registering various components did the trick. The following can be executed from a Command Prompt (Start -> Run -> CMD.EXE):
net stop wuauserv
net start wuauserv
Someone else backed off some of the changes recently introduced to a system, and that enabled Windows Update / Microsoft Update to run successfully - changing the resolution back to 800x600 from 1024x768, and disabling the real-time scanning function of the newly installed anti-virus software did the trick. No word on what AV software was involved...
Another person reported that shutting down services related to McAfee antivirus and using the "Custom" update feature on Microsoft Update enabled him to successfully update his system.
Selectively installing larger items (OS Service Packs, IE, .NET Framework, DirectX, etc) outside of Windows Update / Microsoft Update, and coming back to the Windows Update / Microsoft Update services for the smaller patches worked for another individual.