Apple going DRM-free on a selection of their tracks opens up the possibility of listening to them on a Linux machine without the need of excessive hackery.
The built-in Rythmbox music player can actually play all kinds of music files, but an extra package needs to be installed for them to play the .m4a files that you get from the iTunes store.
The package in question is "gstreamer0.10-plugins-bad-multiverse". This can be installed using synaptic, or with the command:
sudo apt-get install gstreamer0.10-plugins-bad-multiverse
You can then restart Rythmbox (you may need to re-import your .m4a songs), and you should be able to play them just fine.