Most notable is the funnel web spider. And then there is the Redback, which is kind of similar to the Black Widow. Luckily, I did some research when I first got here to start learning about these little buggers so I wouldn't jump sky high every time I saw movement at night. It's still a good idea to be cautious and aware and always check your closed-toed shoes before slipping those feet inside them. This is why I always had shoe boxes... to keep the creepy crawlers outta my shoes!
Plus, i tend to walk in the middle of the neighborhood streets in the evening. It's easier to see things in trees. One night, I was walking with Travis to dinner, and I saw something move above us. I looked up, and casually told him to move left now. I don't know what the spider was, but he was shimmying right down from his huge web and would have been nearly on top of Travis's head had he walked directly under the spider.
The one I see most often is the Huntsman Spider. Now, these guys can get big. The biggest one I've encountered was as big as my hand outstretched! Plus, they move quickly, and they look a little like a cousin to the tarantula! And they love to catch me off guard too. I had the pleasure of finding one on the bathroom wall right by the doorway one morning. I thought I might be stuck in there all day. Here's a quick blurb about the Huntsman with a bit of a comic twist. (Link to Huntsman article)
Another site I found actually explains which ones will kill and which ones are just painful and what to do if one does bite. This helps, but I still jump! (Link to more spider info from the Australian Museum)