There's plenty of iffy ways to get music on the web, but advertising-backed legal download services are often restricted to the US. Qtrax is a Silverlight-based service which is actually accessible in Australia, allowing you to download songs free of charge and play them back on your PC.
Qtrax doesn't specify how many tracks it has available, but my quick search over some well-known and more obscure artists found the coverage reasonable. You can download individual tracks (and have to before you can play them), and add tracks to playlists; there wasn't an obvious option for downloading entire albums in one go.
The big disadvantage of the Qtrax downloads in that they're in DRM-protected WMA format, so you can't easily export them to most portable players or to other platforms. On my quick check through, I found some songs missing from individual albums, occasional track title rendering issues, and some tracks listed as available which popped up a 'Coming soon' message, which is frankly poor behaviour. The 'Buy now' links for MP3 alternatives go through to Amazon, which means they're effectively useless for Australians.
The Qtrax player requires Silverlight and works on Windows and Mac. Right now, the service is active in Australia, New Zealand, the US, Canada, Hong Kong and a handful of other countries.