There are lots of public camera feeds (or streams, whatever you want to call them) availble on the Internet and one of the best places to find them is via the EarthCam website. Otherwise just search Google for, say, "live webcams" (remembering to ignore the adult ones) or download something like Webcam Saver that shows you a whole bunch of streams from around the world as your computer's screen saver (though this software is trialware so you have to pay for it if you want to keep on using it). If you want more specific user-created streams, check out Ustream.Tv and maybe Justin.tv as well.
There are a number of Australian webcams too, and though the live Melbourne skyline camera is currently inoperative, you can see awesome time lapse montages of the city -- showing an hour's worth of photos taken over the previous hour -- on OMNIConnect's Melbourne Webcam page.
For more practical stuff, you have the Port of Melbourne cameras that show you shipping traffic from the Shipping Management Centre in Melbourne and surf conditions from the Port Lonsdale Lighthouse at Point Lonsdale. You can also view the latest traffic conditions within Melbourne on the CityLink website: click on the 'CityLink Webcam' link at the bottom of the right column of the CityLink home page or view all the video streams on this page (which refreshes every ten seconds but doesn't have any labels on the photos).
UPDATE: I wrote about some more webcams in a follow-up post.