I want the ability to download any FLV Video on a web page (not just services like YouTube), I'm using Firefox so an addon is good but an external application would be even better.
If you want to get most any FLV, you can use the Firefox extension "Live HTTP Headers", which shows you the HTTP headers of requests and results.
You can usually find the FLV from just watching those, but its not as easy as just using a program to grab it for you.
Edit: Looking back at this post, if you are using firefox you can also install the "Firebug" extension, which has a "Net" tab that shows all of the network traffic. It is easy to see which is the largest file being loaded and right click and open it in a new tab for download.
The Firefox extension Video Download Helper is incredibly easy to use and works on many, many video sites. As an extra benefit, it works for most kinds of media files (e.g. WMV, WAV, MP3, MP4), not just FLVs. Highly recommended.