I had friends that came across a brown snake they claim it chased them while they were walking on a dirt road. luckily someone in a car saw what was happening and ran the snake over. This didn't kill the snake but it was enough to send the snake in the opposite direction. Snakes don't normally chase people and apart from this case running over them is not a good idea as often they can get caught up under the car and you could take them home with you. I've had a few in my back yard. A couple of times I've found the cat sitting very still having a staring competition with one. The snake has it's reared up and is also keeping very still. Quite scary I've had to pull the cat away risking myself getting bitten. I did read a story in the paper once about a cat and snake staring at each other for days apparently the snake died I think from dehydration.
RE: Life in the remote wilderness - Belair National Park