On every boot, OSX 10.8 always checks the dock for certain apps (Launchpad, Appstore, Reminders, Notes, etc.), and adds them back to the dock if they've been removed. (No idea why--this seems odd & annoying to me, too.)
The solution is to edit the system plist file (/Library/Preferences/com.apple.dockfixup.plist), removing the configuration elements that define these "fixups". To modify this file, you'll need admin privileges--TextWrangler should automatically prompt you, when you start changing things.
In the plist file, find the "add-app" key, which should be followed immediately by an element, which contains several elements:
You can selectively remove just the elements for certain apps, or you can remove them all.
After you save those changes, you'll still have to manually remove the offending dock icons. However, on future reboots, the system will not automatically add those apps back to the dock. (You can always add them back manually, if you want.)