Are you using Sync to Sync the history?

You can check for problems with the places.sqlite database file in the Firefox profile folder.

• http://kb.mozillazine.org/Bookmarks_history_and_toolbar_buttons_not_working_-_Firefox
• https://support.mozilla.org/kb/Bookmarks+not+saved#w_fix-the-bookmarks-file

• Places Maintenance: https://addons.mozilla.org/firefox/addon/places-maintenance/

You can check for problems with the sessionstore.js file in the Firefox profile folder that store session data.

• Help > Troubleshooting Information > Profile Directory: Show Folder (Linux: Open Directory; Mac: Show in Finder)
• http://kb.mozillazine.org/Profile_folder_-_Firefox
• http://kb.mozillazine.org/Multiple_profile_files_created

Deleting sessionstore.js will cause App Tabs and Tab Groups and open and closed (undo) tabs to get lost and you will have to recreate them (make a note or bookmark them if possible).

Thanks, cor-el, but it doesn't look like either places.sqlite or sessionstore.js was the problem. I tried closing the browser, renaming both of those files away and starting the browser again, and the cancelled downloads still showed up.

I am using Sync and syncing history, yes.

Open the Downloads Manager <Control> J. Right click on those entries and select Cancel.

You can check the home page setting:

• Tools > Options > General > Startup: Home page

Firefox supports multiple home pages separated by '|' (pipe) symbols.

• https://support.mozilla.org/kb/How+to+set+the+home+page

You can check for problems with preferences.

Delete possible user.js and numbered prefs-##.js files and rename (or delete) the prefs.js file to reset all prefs to the default value including prefs set via user.js and prefs that are no longer supported in the current Firefox release.

• http://kb.mozillazine.org/Preferences_not_saved
• http://kb.mozillazine.org/Resetting_preferences

Well, I'm not sure what happened but after a few days, the cancelled downloads went away by themselves.