EDIT: Looks like most of the great deals are gone. Though there are still a few around apparently. Keep an eye on the comments.
Crazy cheap price to LA from Sydney or Melbourne (and Brisbane as commented below)
I've plugged in a few dates and seems that there are fares available for most of October and November 2015. Also getting reports for fares this cheap in December and January.
Also, awesome prices to New York, had to work a little harder to find dates for that one.
Adelaide to LA is coming in at about $786AU.
Other reports of fares to London / Paris / San Fran are mentioned in the comments for under $1000.
Try using the search function at http://www.skyscanner.com/ the ability to search the whole month makes it a little easier to find the cheap fares.
UPDATE 2:
Hi everyone, just an update following yesterday’s glitch where mistake fares were incorrectly offered for sale by some US based online travel agents.
Apologies for the confusion. The glitch was fixed at 11:30am AEST, however I'm pleased to let you know that Qantas will honour the bookings in this case.
Woo hoo!
UPDATE:
An update for you savvy AFFers celebrating Xmas in July with these mistake fares: they’re not valid and have been removed from sale. We’re currently following up affected bookings.
Expect bookings to be cancelled shortly.
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Mar 17 -Apr 3rd 2016