hello, firefox 21 & upwards now makes use of the codecs that are included in your OS that enable it to directly play mp3 & mpeg files (also for html5 videos). in order to disable that, enter about:config into the firefox address bar (confirm the info message in case it shows up) & search for the preference named media.windows-media-foundation.enabled. double-click it and change its value to false.

_{Note: The above preference only applies to Windows Vista and higher. Windows Media Foundation isn't available on Windows XP. Starting in Firefox 26, MP3 content on Windows XP will open in the browser with the built-in player using DirectShow; the related preference is media.directshow.enabled (bug 861693). Ref: http://kb.mozillazine.org/File_types_and_download_actions#Built-in_support_for_certain_media AliceWyman}

another way to download the files without tweaking the preference mentioned above would be to right-click the link that leads to a mp3 file or right-click the player in firefox and choose to download the file like that...

edit: for webm you can set media.webm.enabled to false in about:config

It's great that there is a "backdoor" per se to disable this behavior, but I thought that was why there are a ton of file types in the tools/options/applications window to configure? I spent quite a bit of time going through the entire list tweaking the settings of what to play, what to download, and what to ask, only to find out that NONE of them made a difference!

I do very much appreciate that FIrefox is so configurable, but I just wish it wasn't so difficult to figure how to tweak things!

You should be able to save media files played by the built-in HTML5 media player via the right-click context menu (Save Audio As).