This Friday (starting at 22:31 Melbourne daylight savings time, 11:31 UTC), a Centaur booster rocket will crash on the surface of the Moon, closely followed by the spacecraft it helped get there, LCROSS (Lunar Crater Observation and Sensing Satellite). This is expected to be a spectacular event that will create a plume of debris several kilometres high -- and was carefully planned.
The intention of this phase of the LCROSS mission is to look for water near the southern lunar pole, testing the hypothesis that water ice exists at the permanently dark bottom of polar craters. In order to do that, the booster rocket that carried LCROSS (and its cousin LRO) up to the Moon will be made to crash into the crater Cabeus. The resulting plume of debris will then be studied by hundreds of Earth-based observatories, the lunar orbiter LRO, the Hubble Space Telescope... and the LCROSS craft itself, which will fly through the plume, analysing its composition directly. It will then crash on the same crater, four minutes after the booster, generating another (smaller) plume which will be similarly studied from a distance.
One interesting thing to be aware of: the debris plume should be easily seen from the Earth with any moderately-sized telescope (minimum aperture of 10 to 12 inches) as it is illuminated by the Sun (the actual impact won't be visible as it will be hidden by the crater walls). Of course, for this you will need to be on the side of the Earth facing the Moon -- and this does not include Australia. The best place to be is the middle of the Pacific Ocean, in fact, but the west coast of the USA is well located as well (the east coast, as most of South America, will have the Moon on the sky but will also have the Sun).
For Melbourne, the Moon will rise at 1:07am the next day, at which time nothing should be visible (the plume will have long since fallen back onto the surface). The best way to watch the impact, then, will be through NASA TV. NASA has put together an excellent LCROSS viewer's guide which will tell you where to go (and, if you happen to be in one of the right locations, where to look at and how).
More information (much more, in fact) can be found at the main LCROSS mission page.