The (official) native Spotify Linux client got support for free accounts recently. Here is how to install it on Ubuntu and fix some bugs such as not being able to play local music in Ubuntu.
Update: the instructions below should work with Ubuntu 14.04, 13.10, 13.04, 12.10 and 12.04.
Install the native Linux Spotify client under Ubuntu
deb http://repository.spotify.com stable non-free
Once you do this, two repository lines are actually added and the second one (for source code) will display an error when running "sudo apt-get update", so remove this line:
http://repository.spotify.com stable non-free (Source Code)
3. Import the Spotify repository key and install Spotify for Linux:
sudo apt-key adv --keyserver keyserver.ubuntu.com --recv-keys 94558F59
sudo apt-get update
sudo apt-get install spotify-client
That's it! I also recommend using the Spotify Ambiance theme we've covered on WebUpd8, which makes the application integrate better with the Ubuntu desktop (for both the application and its tray icon).