From MozillaZine Knowledge Base

If downloads currently in progress don't appear in the Downloads window:

• Exit Firefox completely, open your profile folder and delete the downloads.rdf file (read this if you have trouble finding it).

If completed downloads don't appear in the Downloads window, make sure you haven't disabled the download history in your Firefox settings [1]:

• Firefox 2: Click "Tools -> Options -> Privacy / History". "Remember what I've downloaded" should be checked.
• Firefox 1.5: Click "Tools -> Options -> Privacy -> Download History". If "Remove files from the Download Manager" shows "Upon successful download", select a different option from the drop-down list.

If the Downloads window doesn't automatically open when you start downloading a file:

• Firefox 2: Click "Tools -> Options -> Main / Downloads" and check "Show the Downloads window when downloading a file".
• Firefox 1.5: Click "Tools -> Options ->Downloads / Download Manager" and check "Show Download Manager when a download begins".