Yes, at T1 (International Terminal) and T2 (Domestic Terminal).
I was there in 2011 but can't remember the details (except that I did use internet connection at the airport). Anyway, Foursquare is a good memory aid, and several tips from 2011 and 2012 say there's indeed wifi available.
February 10, 2012:
Free wifi all over with the "FREE WIFI BY EXPEDIA SYD" network. Just
choose a destination and flight number.
August 24, 2012:
You get free and fast wifi here!
March 11, 2011:
Free wifi in the international terminal (T1)
October 2, 2012:
Aquí el wifi gratis funciona!!!
Update: The Sydney airport website also confirms this:
Free Wi-Fi is available throughout International Terminal (T1) and
Domestic Terminal (T2).
Sydney Airport now provides free Wi-Fi for all travellers at both the
Domestic (T2) and International (T1) Terminals. You can use any Wi-Fi
enabled device to connect including your laptop, smartphone or tablet.
Simply select “Free Internet by sponsors name & SYD” from the list of
available networks, answer the questions, read the terms and
conditions and click "Proceed". You will be shown a sponsored message
then directed to a website.
From there you can browse the internet for up to 2 hours and 500MB of
Coverage is provided throughout the entire International Terminal (T1)
and Domestic Terminal (T2).