On Linux (at least on Ubuntu this is possible), you don't need any special application. Just follow the following procedure:
1. Go to YouTube and watch the video you want to download (like you would normally do)
2. When the video is fully loaded (light red bar 100% full), open the file browser of your choice (for geeks: it can be the terminal, yes 🙂), go to the /tmp folder of your filesystem
3. You will find there a file named Flash******** (where ******** is some group of numbers and letters). This file is actually an MP4 file with the video. It will be deleted once you leave the YouTube page.
4. Copy the file to a folder of your choice and rename the file (preferably, put it with a .mp4 extension at the end so it can be recognized by other systems).
5. Done! The video is now downloaded.
I download music this way. I watch the music video, the copy it from the /tmp folder to my videos folder, and convert it to MP3 using WinFF (GUI for FFmpeg).
+rep me if you enjoyed this guide. Not copied&pasted, written originally for FP and based in similar guides from lots of other sites. I have done this procedure lots of times with no problems 🙂