Somehow I have got the Adobe Download Manager installed on my PC, and it opens up periodically. I don't know what triggers it.
How can I get rid of it?
It should appear in Add/Remove Programs (or "Programs and Features", depending on your version of Windows). Select it and uninstall.
Note that you'll probably have to use it again if you're updating or installing Flash or Reader.
It seems it was opening when I opened Firefox. Adobe seems to have silently installed an add-in for it :-( Bad Adobe! Bad! No doughnut! Bad!
Deleting the add-in seems to have gotten rid of that annoying window.