How to rip an mp3 audio from YouTube video...

Packages required, ffmpeg and libavcodec-extra-52

$ sudo apt-get install ffmpeg libavcodec-extra-52

The easiest way is to run the command below. Note that -ab is an option for audio bitrate

$ ffmpeg -i uverworld.flv -ab 192k uverworld.mp3

If you prefer GUI, you can use VLC. Below is a step by step screenshots

Click save item in playlist

Select mp3 profile and click Start button

If you want to change audio bitrate, click edit profile button, set bitrate, Save changes and Start the process

Note:
Tested on Linux Mint 10 64-bit.

How to download YouTube videos on Linux...

Package required, youtube-dl

    $ sudo apt-get install youtube-dl

Command to download

    $ youtube-dl [options] video_url

If you're getting an error as "ERROR: unable to download video (format may not be available)", get latest version of youtube-dl from github.

Set execute permission

    $ chmod +x youtube-dl-latest

Execute the latest version script to download video

    $ ./youtube-dl-latest [options] video_url

Note:
Tested on Linux Mint 10 64-bit.

Update (13/03/2011)
Found out an easy way. Install video download helper addon for Mozilla Firefox. Works perfectly on both Linux and Windows.