It has HDMI and Optical outputs that you can use to feed your amp’s etc. to listen to your media files. So throw away your CD player (and your DVD player!) – I donated mine already!
The WDTV Live has built in access to Pandora & LIve365. I had never used Pandora until I got my WDL and now I am hooked on it. You set up an account on your PC, set up a very easy music preference, then forget the PC and liste direct from the WD Live. Pandora gives (I believe 40 hours of free music per month) or you can subscribe for $36/year.
The WDTV Live also supports YouTube direct/native.
There is no other native “browser” for you to access generic music streaming, however, there are 3rd Party products that you run on an always-on PC to host up streaming services. Play-On for example will host up your Netflix instant queue to play on the WD TV Live – but that has a fee/subscription for the service (after a free trial). I don’t use it enough to make it worth the purchase.