Server-managed computers work differently
After struggling with this nonsense for a while and entertaining myself with the amazingly diverse experiences reported in this thread, a co-worker discovered a comment on the web to the effect that the problem might be due to preferences enforced on managed machines by their OS X Server. This solved the problem for us. If you can't get rid of the problem and your computer is not managed by an OS X Server, then maybe one of the other solutions suggested earlier in this thread will work.
Do one of the following, then killall Dock:
[Q&D] The offending file is /Library/Managed Preferences/com.apple.Dock.plist. Supposedly this is created when a user logs in on a managed computer for the first time, but the 10.6.6 update somehow caused this to happen to existing user accounts.
[Workgroup Manager] The root cause of this for managed computers is found in the Preferences section of Workgroup Manager. Go there and click the Dock icon. If you select a user or group, you'll see these applications in the "Place these items in the user's Dock" section. Strangely, the radio button above where they show up is set to "Never", where the described effects would correspond to "Once"; furthermore, the items are grayed out. To get around this, select "Once" and delete all the offending items (you can select multiply, then click the -).
I found that doing this for all the groups and not bothering with the users was sufficient to solve the problem for most users. For at least one user, and I haven't figured out why, I had to delete these applications for the user specifically, not just the group.
After a user does "killall Dock" the added applications will not just be (re)movable, but they won't even be there (unless they were already on the user's Dock, in which case they will retain the user's positioning rather than forcing them all the way to the left).
You can find the relevant information about adding items to a user's doc on the page named "To add items to a user's Dock" either in Workgroup Manager Help, or on page 188 of Apple's
User Management document.