Amarok, by default, does not come with the MP3 codecs installed. This is for a variety of reasons that I’m not going to go in to here.
To get MP3s working in amarok, or to listen to internet radio, you need to install the libxine1-ffmpeg package. In ubuntu, that means doing the following:
sudo apt-get install libxine1-ffmpeg
Restart Amarok (if it’s open) and voila.