Firefox's separate downloads window can get kind of annoying, especially if you don't have the screen space to be moving windows around. The Downloads in Tab extension will let you monitor those downloads in a tab, Google Chrome-style.
If you've switched from Chrome to Firefox, but you miss seeing your downloads in a new tab, this extension will help ease your mind. Just install the extension, and all further downloads will open a new tab in your tab bar, just like in Chrome — you'll be able to monitor them, open them when they're finished, and clear the list right from there. You can even customise where the tab shows up and whether it automatically focuses by going into the extension's preferences.
Downloads in Tab is a free download for Firefox only. If you'd like even more space-savings, you can also check out Download Statusbar, which puts those downloads — you guessed it — down near your status bar.