Melbourne is a relatively safe place to visit, but you should still take reasonable precautions. Don't leave hotel rooms or cars unlocked, and don't leave money, wallets, purses or cameras unattended or in full view through car windows.
But when it comes right down to it, it's the trams you have to watch out for. Be extremely cautious when stepping on and off trams - a lot of people have been hit by passing cars, so don't step off without looking both ways. Pedestrians in Bourke St Mall should look for passing trams too. Car drivers should treat trams with caution, and never pass on the inside when a tram has stopped. Cyclists should be careful not to get their wheels caught in tram tracks, and motorcyclists should take care when tram tracks are wet. Hook turns (making a right turn from the left-hand lane at some city-centre intersections so as not to obstruct tram tracks) are a Melbourne speciality and take a bit of getting used to.