The Download Statusbar add-on for Firefox offers a less intrusive, more streamlined way to keep track of your downloads than the standard downloads window.
Instead of displaying your downloads in the regular pop-up window, Download Statusbar tracks them in a new toolbar that displays at the bottom of the browser. A progress meter shows the ETA and speed for current downloads.
When you double-click a completed download, or right-click and choose the Open Containing Folder option, the toolbar listing for that download automatically clears. When there's nothing remaining in the toolbar, it automatically hides. To see your download history, you can still open the regular downloads window, but it otherwise won't pop up on its own.
Download Statusbar makes it easy to track in-progress downloads as you continue to surf, and smooths out the browsing experience by sparing you a separate window. This well-designed extension makes a fine addition to Firefox.
Note: The download link takes you to Download Statusbar's add-on page at Mozilla.org, where you can install the extension directly into Firefox. The add-on is free to use, but its creator requests a donation.