Every country is different, and it's important to do your homework on where you're traveling to. A wonderful source to do this is the U.S. Department of State’s official website, Travel.State.Gov, which provides detailed information on every country around the world, including information on safety and security conditions, crime, health and medical considerations, local laws and areas to avoid.
Search "Australia," for instance, and you'll learn things like "Although U.S citizens are not specifically targeted for crime, you should be aware that robberies, burglaries, assault, and auto theft are common in Australia’s larger cities" and "Be careful when visiting bars or clubs in the entertainment areas of major cities, as 'bar brawls' and other assaults sometimes occur. Also, watch out for drink spiking when consuming alcohol with unfamiliar people."
It's also recommended that you know the location of the closest U.S. embassy or consulate in the destination you're venturing to.