Application ROM Manager is uninstalled, but market wants to update it every day I uninstalled ROM Manager. Since I did so, I've received daily notifications from the Market saying there's an update.

I've logged into the market via the desktop browser and ROM manager is not listed as an installed application. (Though many I have uninstalled ages ago are listed, but that's another matter).

The notifications are annoying. How can I kill ROM Manager once and for all?

HTC Desire running Cyanogenmod7
ROM Manager shouldn't be a required Systems app to run CyanogenMod.  Take a look at the steps over here to remove a system app from your phone: http://oldwiki.cyanogenmod.org/wiki/Barebones

Something like:

adb remount 
adb shell rm -f /system/app/RomManager.apk