The 108' long, 165 ton coal-fired steam tug Waratah (1902) (originally named Burunda) was built at the Cockatoo Island dockyard and was used to tow barges and dredges along the NSW coast. Acquired by the Sydney Heritage Fleet in 1968, she was rebuilt and is now the oldest tug in working order in Australia.

Here we see her at the Sydney International Boat Show, working up a head of steam, surrounded by somewhat more modern vessels for the most part.

To see her in action, refer to image 081213_141912_2763 in this gallery.
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Edit Jul 2024: There is a lot of lost history in this shot. The Imax Theatre was torn down in 2016 (though subsequently rebuilt as part of a new hotel tower). The University of Technology tower (at roughly the 11 o'clock position) is still there on Broadway, but the Convention Centre (roughly 2 o'clock) has been torn down and replaced, and Harbourside shopping Centre on the right has gone as well. At some point I should probably go and take another shot here just for comparison's sake.