This is just niggling away at me. There's a FAQ in the Chromecast Product forums about how to play music that's in your iTunes library. The answer given is to upload it all to Google Play Music and play it from there. There's numerous reasons why you might not want to do that. Not least of it is why you should upload it to the cloud to then download it again when it's on the same LAN on a network share or NAS. Then there's the need to sync some or all of it to an iPod. And the limit of 20k tracks. And the limited file formats and need to transcode from say FLAC to 320 MP3. Or the lack of support for .m3u or .pls playlists. There's lots of reasons why you would want to keep a local library of music and to normally play it locally in a laptop application like iTunes, Windows Media Player, VLC, Winamp, Mediamonkey, Amarok or whatever. 

What's not mentioned in the FAQ is that there is a kind of solution available already in the Beta Chrome Cast extension. You can choose "Cast Screen/Window (Experimental), then choose whole screen and it will cast the audio as well. So you can play in iTunes in the normal way, Cast from Chrome and have the music come out of the TV as well as the local speakers.

There's been a suggestion that this might chnage with Cast for Audio. But this looks like it will be a built in Chromecast in wireless speakers so it extends the hardware, player end but doesn't look like it will make it any easier to play from iTunes. It's not hear yet so maybe that will change.

So this begins to look like Google embracing and extending; using one product to force you into using their other products. Google Play Music still has merit but it's annoying that you're being forced too use it. It's the same problem as with Chromebooks being unable to play from local network shares and the same solution being provided as an answer.

The question though is what to do about it.
- Apple is never going to do this themselves. So the solution either has to be a generic audio grab by Google or a 3rd party iTunes extension.
- Same for Windows Media Player. There is a possibility here that Google help Chromecast to become a DLNA Renderer. WMP can "Play To" one of these.
- Logitech Media Server. There is some interest in making Chromecast a target. Probably not going to happen soon. You can play the LMS stream in Chrome and then cast the tab and that works. The only problem being that Chrome's support for <audio> and mp3 streaming has a 70s buffer. So if you change tracks, the audio doesn't change for 70s. Chrome audio can't pick up the 
- VLC have a stated intention to support Chromecast. It looks like this may turn up in v2.2 and allegedly youn can do this now in the Release Candidates.
- Winamp. Winamp development has effectively died even though Radionomy has take it on from AOL. It might be possible for a 3rd party to write an output plugin for the Chromecast.
- Other media players. There is some interest from Mediamonkey and Foobar to support Chromecast. Google could support this. There's also interest from the same places in the more generic solution of a DLNA Renderer. 

Perhaps the best solution is that the Chrome Cast extension is enhanced so it can grab and cast the audio/video from a single application window on the desktop. The other is to build an audio device driver for Windows and OSX but that's going to be more awkward if you want to swap quickly from local speakers to Chromecast and TV speakers and back again.

Listen to music in your iTunes library
https://productforums.google.com/forum/#!category-topic/chromecast/ewDqB_eGoLo
https://productforums.google.com/d/msg/chromecast/I7WU0Y3GLac/-eddisYt_lgJ